RFC5053 日本語訳
5053 Raptor Forward Error Correction Scheme for Object Delivery. M.Luby, A. Shokrollahi, M. Watson, T. Stockhammer. October 2007. (Format: TXT=113743 bytes) (Status: PROPOSED STANDARD)
プログラムでの自動翻訳です。
英語原文
Network Working Group M. Luby
Request for Comments: 5053 Digital Fountain
Category: Standards Track A. Shokrollahi
EPFL
M. Watson
Digital Fountain
T. Stockhammer
Nomor Research
October 2007
Lubyがコメントのために要求するワーキンググループM.をネットワークでつないでください: 5053年のデジタル噴水カテゴリ: 標準化過程A.Shokrollahi EPFL M.ワトソンDigital噴水T.Stockhammer Nomor研究2007年10月
Raptor Forward Error Correction Scheme for Object Delivery
物の配送の猛きん類前進型誤信号訂正計画
Status of This Memo
このメモの状態
This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards" (STD 1) for the standardization state and status of this protocol. Distribution of this memo is unlimited.
このドキュメントは、インターネットコミュニティにインターネット標準化過程プロトコルを指定して、改良のために議論と提案を要求します。 このプロトコルの標準化状態と状態への「インターネット公式プロトコル標準」(STD1)の現行版を参照してください。 このメモの分配は無制限です。
Abstract
要約
This document describes a Fully-Specified Forward Error Correction (FEC) scheme, corresponding to FEC Encoding ID 1, for the Raptor forward error correction code and its application to reliable delivery of data objects.
このドキュメントはFullyによって指定されたForward Error Correction(FEC)計画について説明します、FEC Encoding ID1に対応しています、Raptor前進型誤信号訂正コードとデータ・オブジェクトの信頼できる配信へのその適用のために。
Raptor is a fountain code, i.e., as many encoding symbols as needed can be generated by the encoder on-the-fly from the source symbols of a source block of data. The decoder is able to recover the source block from any set of encoding symbols only slightly more in number than the number of source symbols.
猛きん類が噴水コードである、すなわち、シンボルを必要とされるのと同じくらい多くコード化するのがエンコーダでデータの1つのソースブロックのソースシンボルから急いで発生できます。 デコーダはソースシンボルの数より数における、シンボルをわずかにだけコード化するどんなセットからもソースブロックを取り戻すことができます。
The Raptor code described here is a systematic code, meaning that all the source symbols are among the encoding symbols that can be generated.
ここで説明されたRaptorコードはシステマティック・コードです、発生できるコード化シンボルの中にすべてのソースシンボルがあることを意味して。
Luby, et al. Standards Track [Page 1] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[1ページ]。
Table of Contents
目次
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Requirements Notation . . . . . . . . . . . . . . . . . . . . 3
3. Formats and Codes . . . . . . . . . . . . . . . . . . . . . . 3
3.1. FEC Payload IDs . . . . . . . . . . . . . . . . . . . . . 3
3.2. FEC Object Transmission Information (OTI) . . . . . . . . 4
3.2.1. Mandatory . . . . . . . . . . . . . . . . . . . . . . 4
3.2.2. Common . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2.3. Scheme-Specific . . . . . . . . . . . . . . . . . . . 5
4. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1. Content Delivery Protocol Requirements . . . . . . . . . . 5
4.2. Example Parameter Derivation Algorithm . . . . . . . . . . 6
5. Raptor FEC Code Specification . . . . . . . . . . . . . . . . 8
5.1. Definitions, Symbols, and Abbreviations . . . . . . . . . 8
5.1.1. Definitions . . . . . . . . . . . . . . . . . . . . . 8
5.1.2. Symbols . . . . . . . . . . . . . . . . . . . . . . . 9
5.1.3. Abbreviations . . . . . . . . . . . . . . . . . . . . 11
5.2. Overview . . . . . . . . . . . . . . . . . . . . . . . . . 11
5.3. Object Delivery . . . . . . . . . . . . . . . . . . . . . 12
5.3.1. Source Block Construction . . . . . . . . . . . . . . 12
5.3.2. Encoding Packet Construction . . . . . . . . . . . . . 14
5.4. Systematic Raptor Encoder . . . . . . . . . . . . . . . . 15
5.4.1. Encoding Overview . . . . . . . . . . . . . . . . . . 15
5.4.2. First Encoding Step: Intermediate Symbol Generation . 16
5.4.3. Second Encoding Step: LT Encoding . . . . . . . . . . 20
5.4.4. Generators . . . . . . . . . . . . . . . . . . . . . . 21
5.5. Example FEC Decoder . . . . . . . . . . . . . . . . . . . 23
5.5.1. General . . . . . . . . . . . . . . . . . . . . . . . 23
5.5.2. Decoding a Source Block . . . . . . . . . . . . . . . 23
5.6. Random Numbers . . . . . . . . . . . . . . . . . . . . . . 28
5.6.1. The Table V0 . . . . . . . . . . . . . . . . . . . . . 28
5.6.2. The Table V1 . . . . . . . . . . . . . . . . . . . . . 29
5.7. Systematic Indices J(K) . . . . . . . . . . . . . . . . . 30
6. Security Considerations . . . . . . . . . . . . . . . . . . . 43
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 43
8. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 44
9. References . . . . . . . . . . . . . . . . . . . . . . . . . . 44
9.1. Normative References . . . . . . . . . . . . . . . . . . . 44
9.2. Informative References . . . . . . . . . . . . . . . . . . 44
1. 序論. . . . . . . . . . . . . . . . . . . . . . . . . 3 2。 要件記法. . . . . . . . . . . . . . . . . . . . 3 3 形式とコード. . . . . . . . . . . . . . . . . . . . . . 3 3.1。 FEC有効搭載量ID. . . . . . . . . . . . . . . . . . . . . 3 3.2。 FEC物のトランスミッション情報(OTI). . . . . . . . 4 3.2.1。 義務的である、.43.2 .2。 コモン. . . . . . . . . . . . . . . . . . . . . . . . 4 3.2.3。 計画特有の.5 4。 手順. . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.1。 内容物配送プロトコル要件. . . . . . . . . . 5 4.2。 例のパラメタ誘導アルゴリズム. . . . . . . . . . 6 5。 猛きん類FECは仕様. . . . . . . . . . . . . . . . 8 5.1をコード化します。 定義、シンボル、および略語. . . . . . . . . 8 5.1.1。 定義. . . . . . . . . . . . . . . . . . . . . 8 5.1.2。 シンボル. . . . . . . . . . . . . . . . . . . . . . . 9 5.1.3。 略語. . . . . . . . . . . . . . . . . . . . 11 5.2。 概観. . . . . . . . . . . . . . . . . . . . . . . . . 11 5.3。 物の配送. . . . . . . . . . . . . . . . . . . . . 12 5.3.1。 ソースブロック工事. . . . . . . . . . . . . . 12 5.3.2。 パケット工事. . . . . . . . . . . . . 14 5.4をコード化します。 系統的な猛きん類エンコーダ. . . . . . . . . . . . . . . . 15 5.4.1。 概観. . . . . . . . . . . . . . . . . . 15 5.4.2をコード化します。 最初のコード化ステップ: 中間的シンボル世代. 16 5.4.3。 第2コード化ステップ: LTコード化. . . . . . . . . . 20 5.4.4。 ジェネレータ. . . . . . . . . . . . . . . . . . . . . . 21 5.5。 例のFECデコーダ. . . . . . . . . . . . . . . . . . . 23 5.5.1。 一般、.235.5 .2。 ソースブロック. . . . . . . . . . . . . . . 23 5.6を解読します。 乱数. . . . . . . . . . . . . . . . . . . . . . 28 5.6.1。 テーブルV0. . . . . . . . . . . . . . . . . . . . . 28 5.6.2。 テーブルV1. . . . . . . . . . . . . . . . . . . . . 29 5.7 系統的なインデックスリストJ(K). . . . . . . . . . . . . . . . . 30 6。 セキュリティ問題. . . . . . . . . . . . . . . . . . . 43 7。 IANA問題. . . . . . . . . . . . . . . . . . . . . 43 8。 承認. . . . . . . . . . . . . . . . . . . . . . . 44 9。 参照. . . . . . . . . . . . . . . . . . . . . . . . . . 44 9.1。 引用規格. . . . . . . . . . . . . . . . . . . 44 9.2。 有益な参照. . . . . . . . . . . . . . . . . . 44
Luby, et al. Standards Track [Page 2] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[2ページ]。
1. Introduction
1. 序論
This document specifies an FEC Scheme for the Raptor forward error correction code for object delivery applications. The concept of an FEC Scheme is defined in [RFC5052] and this document follows the format prescribed there and uses the terminology of that document. Raptor Codes were introduced in [Raptor]. For an overview, see, for example, [CCNC].
このドキュメントは物の配送アプリケーションとしてRaptor前進型誤信号訂正コードにFEC Schemeを指定します。 FEC Schemeの概念が[RFC5052]で定義されて、このドキュメントは、そこに定められた形式に続いて、そのドキュメントの用語を使用します。 [猛きん類]で猛きん類Codesを導入しました。 概観に関しては、例えば、見てください[CCNC]。
The Raptor FEC Scheme is a Fully-Specified FEC Scheme corresponding to FEC Encoding ID 1.
Raptor FEC SchemeはFEC Encoding ID1に対応するFullyによって指定されたFEC Schemeです。
Raptor is a fountain code, i.e., as many encoding symbols as needed can be generated by the encoder on-the-fly from the source symbols of a block. The decoder is able to recover the source block from any set of encoding symbols only slightly more in number than the number of source symbols.
猛きん類が噴水コードである、すなわち、シンボルを必要とされるのと同じくらい多くコード化するのがエンコーダで1ブロックのソースシンボルから急いで発生できます。 デコーダはソースシンボルの数より数における、シンボルをわずかにだけコード化するどんなセットからもソースブロックを取り戻すことができます。
The code described in this document is a systematic code, that is, the original source symbols can be sent unmodified from sender to receiver, as well as a number of repair symbols. For more background on the use of Forward Error Correction codes in reliable multicast, see [RFC3453].
本書では説明されたコードがシステマティック・コードである、すなわち、送付者から受信機まで変更されていなく一次資料シンボルを送ることができます、多くの修理シンボルと同様に。 信頼できるマルチキャストにおけるForward Error Correctionコードの使用での、より多くのバックグラウンドに関しては、[RFC3453]を見てください。
The code described here is identical to that described in [MBMS].
ここで説明されたコードは[MBMS]で説明されたそれと同じです。
2. Requirements Notation
2. 要件記法
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119].
キーワード“MUST"、「必須NOT」が「必要です」、“SHALL"、「」、“SHOULD"、「「推薦され」て、「5月」の、そして、「任意」のNOTは[RFC2119]で説明されるように本書では解釈されることであるべきですか?
3. Formats and Codes
3. 形式とコード
3.1. FEC Payload IDs
3.1. FEC有効搭載量ID
The FEC Payload ID MUST be a 4 octet field defined as follows:
FEC Payload IDは以下の通り定義された4八重奏分野であるに違いありません:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Number | Encoding Symbol ID |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | ソース街区番号| Symbol IDをコード化します。| +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 1: FEC Payload ID format
図1: FEC有効搭載量ID形式
Luby, et al. Standards Track [Page 3] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[3ページ]。
Source Block Number (SBN), (16 bits): An integer identifier for
the source block that the encoding symbols within the packet
relate to.
(16ビット)のソースBlock Number(SBN): パケットの中のコード化シンボルが関連するソースブロックで整数識別子。
Encoding Symbol ID (ESI), (16 bits): An integer identifier for the
encoding symbols within the packet.
Symbol ID(ESI)をコード化する(16ビット): パケットの中のコード化シンボルのための整数識別子。
The interpretation of the Source Block Number and Encoding Symbol Identifier is defined in Section 5.
Source Block NumberとEncoding Symbol Identifierの解釈はセクション5で定義されます。
3.2. FEC Object Transmission Information (OTI)
3.2. FEC物のトランスミッション情報(OTI)
3.2.1. Mandatory
3.2.1. 義務的
The value of the FEC Encoding ID MUST be 1 (one), as assigned by IANA (see Section 7).
IANAによって割り当てられるようにFEC Encoding IDの値は1でなければなりません(1)(セクション7を見てください)。
3.2.2. Common
3.2.2. 一般的
The Common FEC Object Transmission Information elements used by this FEC Scheme are:
このFEC Schemeによって使用されたCommon FEC Object Transmission情報要素は以下の通りです。
- Transfer Length (F)
- 転送の長さ(F)
- Encoding Symbol Length (T)
- シンボルの長さをコード化します。(T)
The Transfer Length is a non-negative integer less than 2^^45. The Encoding Symbol Length is a non-negative integer less than 2^^16.
Transfer Lengthは非負の整数2未満^^45です。 Encoding Symbol Lengthは非負の整数2未満^^16です。
The encoded Common FEC Object Transmission Information format is shown in Figure 2.
コード化されたCommon FEC Object Transmission情報書式は図2に示されます。
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Transfer Length |
+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | Reserved |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol Length |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | 転送の長さ| + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | | 予約されます。| +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | シンボルの長さをコード化します。| +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 2: Encoded Common FEC OTI for Raptor FEC Scheme
図2: 猛きん類FECのためのコード化された一般的なFEC OTIは計画します。
NOTE 1: The limit of 2^^45 on the transfer length is a consequence
of the limitation on the symbol size to 2^^16-1, the limitation on
the number of symbols in a source block to 2^^13, and the
注意1: そして転送の長さにおける2^^45の限界は2^^16-1へのシンボルサイズにおける制限の結果です、2^^13へのソースブロックのシンボルの数における制限。
Luby, et al. Standards Track [Page 4] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[4ページ]。
limitation on the number of source blocks to 2^^16. However, the
Transfer Length is encoded as a 48-bit field for simplicity.
2^^16へのソースブロックの数における制限。 しかしながら、Transfer Lengthは簡単さのための48ビットの分野としてコード化されます。
3.2.3. Scheme-Specific
3.2.3. 計画特有です。
The following parameters are carried in the Scheme-Specific FEC Object Transmission Information element for this FEC Scheme:
以下のパラメタはこのFEC SchemeのためにScheme特有のFEC Object Transmission情報要素で運ばれます:
- The number of source blocks (Z)
- ソースブロックの数(Z)
- The number of sub-blocks (N)
- サブブロックの数(N)
- A symbol alignment parameter (Al)
- シンボル整列パラメタ(アル)
These parameters are all non-negative integers. The encoded Scheme- specific Object Transmission Information is a 4-octet field consisting of the parameters Z (2 octets), N (1 octet), and Al (1 octet) as shown in Figure 3.
すべてこれらのパラメタは非負の整数です。 コード化されたScheme特定のObject Transmission情報は図3に示されるようにパラメタのZ(2つの八重奏)、N(1つの八重奏)、およびアル(1つの八重奏)から成る4八重奏の分野です。
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Z | N | Al |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | Z| N| アル| +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: Encoded Scheme-Specific FEC Object Transmission Information
図3: コード化された計画特有のFEC物のトランスミッション情報
The encoded FEC Object Transmission Information is a 14-octet field consisting of the concatenation of the encoded Common FEC Object Transmission Information and the encoded Scheme-Specific FEC Object Transmission Information.
コード化されたFEC Object Transmission情報はコード化されたCommon FEC Object Transmission情報とコード化されたScheme特有のFEC Object Transmission情報の連結から成る14八重奏の分野です。
These three parameters define the source block partitioning as described in Section 5.3.1.2.
これらの3つのパラメタがセクション5.3.1で.2に説明されるソースブロック仕切りを定義します。
4. Procedures
4. 手順
4.1. Content Delivery Protocol Requirements
4.1. 内容物配送プロトコル要件
This section describes the information exchange between the Raptor FEC Scheme and any Content Delivery Protocol (CDP) that makes use of the Raptor FEC Scheme for object delivery.
このセクションは物の配送にRaptor FEC Schemeを利用するRaptor FEC SchemeとどんなContent Deliveryプロトコル(CDP)の間の情報交換について説明します。
The Raptor encoder and decoder for object delivery require the following information from the CDP:
物の配送のためのRaptorエンコーダとデコーダはCDPからの以下の情報を必要とします:
- The transfer length of the object, F, in bytes
- 物の転送の長さ、バイトによるF
Luby, et al. Standards Track [Page 5] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[5ページ]。
- A symbol alignment parameter, Al
- シンボル整列パラメタ、アル
- The symbol size, T, in bytes, which MUST be a multiple of Al
- シンボルサイズ、バイトによるT。(そのTはアルの倍数であるに違いありません)。
- The number of source blocks, Z
- ソースブロック、Zの数
- The number of sub-blocks in each source block, N
- それぞれのソースブロック、Nのサブブロックの数
The Raptor encoder for object delivery additionally requires:
物の配送のためのRaptorエンコーダはさらに、以下を必要とします。
- the object to be encoded, F bytes
- コード化されたFバイトである物
The Raptor encoder supplies the CDP with the following information for each packet to be sent:
Raptorエンコーダは各パケットが送られる以下の情報をCDPに供給します:
- Source Block Number (SBN)
- ソース街区番号(SBN)
- Encoding Symbol ID (ESI)
- Symbol IDをコード化します。(ESI)
- Encoding symbol(s)
- シンボルをコード化します。(s)
The CDP MUST communicate this information to the receiver.
CDP MUSTはこの情報を受信機に伝えます。
4.2. Example Parameter Derivation Algorithm
4.2. 例のパラメタ誘導アルゴリズム
This section provides recommendations for the derivation of the three transport parameters, T, Z, and N. This recommendation is based on the following input parameters:
このセクションは3つの輸送パラメタの派生のための推薦を提供します、T、Z、N.This推薦は以下の入力パラメタに基づいています:
- F the transfer length of the object, in bytes
- Fはバイトで表現される物の転送の長さです。
- W a target on the sub-block size, in bytes
- Wはバイトで表現されるサブブロック・サイズの目標です。
- P the maximum packet payload size, in bytes, which is assumed to
be a multiple of Al
- Pはアルの倍数であると思われるバイトで表現される最大のパケットペイロードサイズです。
- Al the symbol alignment parameter, in bytes
- アルはバイトで表現されるシンボル整列パラメタです。
- Kmax the maximum number of source symbols per source block.
- ソースの最大数が1ソースブロック単位で象徴するKmax。
Note: Section 5.1.2 defines Kmax to be 8192.
以下に注意してください。 セクション5.1 .2 8192年になるように、Kmaxを定義します。
- Kmin a minimum target on the number of symbols per source block
- Kminはソースブロックあたりのシンボルの数の最小の目標です。
- Gmax a maximum target number of symbols per packet
- Gmaxは1パケットあたりのシンボルの最大の目標番号です。
Luby, et al. Standards Track [Page 6] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[6ページ]。
Based on the above inputs, the transport parameters T, Z, and N are calculated as follows:
上記の入力に基づいて、輸送パラメタT、Z、およびNは以下の通り計算されます:
Let
貸されます。
G = min{ceil(P*Kmin/F), P/Al, Gmax}
G=分ceil(P*Kmin/F)、P/アル、Gmax
T = floor(P/(Al*G))*Al
Tは床(P/(アル*G))*アルと等しいです。
Kt = ceil(F/T)
Ktはceilと等しいです。(F/T)
Z = ceil(Kt/Kmax)
Zはceilと等しいです。(Kt/Kmax)
N = min{ceil(ceil(Kt/Z)*T/W), T/Al}
N=分ceil(ceil(Kt/Z)*T/W)、T/アル
The value G represents the maximum number of symbols to be transported in a single packet. The value Kt is the total number of symbols required to represent the source data of the object. The values of G and N derived above should be considered as lower bounds. It may be advantageous to increase these values, for example, to the nearest power of two. In particular, the above algorithm does not guarantee that the symbol size, T, divides the maximum packet size, P, and so it may not be possible to use the packets of size exactly P. If, instead, G is chosen to be a value that divides P/Al, then the symbol size, T, will be a divisor of P and packets of size P can be used.
値Gは、単一のパケットで輸送されるためにシンボルの最大数を表します。 値のKtは物に関するソースデータを表すのに必要であるシンボルの総数です。 上で引き出されたGとNの値は下界であるとみなされるべきです。 例えば、2の最も近いパワーにこれらの値を増加させるのは有利であるかもしれません。 特に、上のアルゴリズムは、ちょうどサイズP.Ifのパケットを使用するのがシンボルサイズ(T)は最大のパケットサイズを分割します、Pによって可能でないかもしれないことを保証しません、そして、代わりに、P/アルを分割する値になるようにGを選んでいます、そして、次に、シンボルサイズ(T)はPの除数になるでしょう、そして、サイズPのパケットは使用できます。
The algorithm above and that defined in Section 5.3.1.2 ensure that the sub-symbol sizes are a multiple of the symbol alignment parameter, Al. This is useful because the XOR operations used for encoding and decoding are generally performed several bytes at a time, for example, at least 4 bytes at a time on a 32-bit processor. Thus, the encoding and decoding can be performed faster if the sub- symbol sizes are a multiple of this number of bytes.
上のアルゴリズムとサブシンボルが大きさで分ける.2が確実にするセクション5.3.1で定義されたそれはシンボル整列パラメタ(アル)の倍数です。 コード化と解読に使用されるXOR操作が一度に、例えば一般に数バイト実行されるので、これは役に立ちます、一度に32ビットのプロセッサの少なくとも4バイト。 したがって、サブシンボルサイズがこのバイト数の倍数であるなら、より速くコード化と解読を実行できます。
Recommended settings for the input parameters, Al, Kmin, and Gmax are as follows: Al = 4, Kmin = 1024, Gmax = 10.
入力のパラメタ、アル、Kmin、およびGmaxにおけるお勧めの設定は以下の通りです: アル=4、Kmin=1024、Gmax=10。
The parameter W can be used to generate encoded data that can be decoded efficiently with limited working memory at the decoder. Note that the actual maximum decoder memory requirement for a given value of W depends on the implementation, but it is possible to implement decoding using working memory only slightly larger than W.
限られたワーキングメモリがデコーダにある状態で効率的に解読できるコード化されたデータを発生させるのにパラメタWを使用できます。 Wの与えられた値のための実際の最大のデコーダメモリ要件が実現によりますが、Wよりわずかにだけ大きい状態でワーキングメモリを使用する解読を実行するのが可能であることに注意してください。
Luby, et al. Standards Track [Page 7] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[7ページ]。
5. Raptor FEC Code Specification
5. 猛きん類FECコード仕様
5.1. Definitions, Symbols, and Abbreviations
5.1. 定義、シンボル、および略語
5.1.1. Definitions
5.1.1. 定義
For the purposes of this specification, the following terms and definitions apply.
この仕様の目的のために、以下の用語と定義は申し込まれます。
Source block: a block of K source symbols that are considered
together for Raptor encoding purposes.
ソースブロック: 目的をコード化するRaptorのために一緒に考えられる1ブロックのKソースシンボル。
Source symbol: the smallest unit of data used during the encoding
process. All source symbols within a source block have the same
size.
ソースシンボル: コード化の間に使用されるデータの最小単位は処理されます。 ソースブロックの中のすべてのソースシンボルには、同じサイズがあります。
Encoding symbol: a symbol that is included in a data packet. The
encoding symbols consist of the source symbols and the repair
symbols. Repair symbols generated from a source block have the
same size as the source symbols of that source block.
シンボルをコード化します: データ・パケットに含まれているシンボル。 コード化シンボルはソースシンボルと修理シンボルから成ります。 ソースブロックから発生する修理シンボルはそのソースブロックのソースシンボルと同じサイズを持っています。
Systematic code: a code in which all the source symbols may be
included as part of the encoding symbols sent for a source block.
システマティック・コード: すべてのソースシンボルがコード化シンボルの一部として含まれるかもしれないコードはソースブロックに発信しました。
Repair symbol: the encoding symbols sent for a source block that
are not the source symbols. The repair symbols are generated
based on the source symbols.
シンボルを修理してください: コード化シンボルはソースシンボルではなく、ソースブロックに発信しました。 修理シンボルはソースシンボルに基づいて発生します。
Intermediate symbols: symbols generated from the source symbols
using an inverse encoding process . The repair symbols are then
generated directly from the intermediate symbols. The encoding
symbols do not include the intermediate symbols, i.e.,
intermediate symbols are not included in data packets.
中間的シンボル: シンボルは、ソースから過程をコード化する逆を使用することでシンボルを発生させました。次に、修理シンボルは直接中間的シンボルから発生します。 コード化シンボルは中間的シンボルを含んでいません、すなわち、中間的シンボルがデータ・パケットに含まれていません。
Symbol: a unit of data. The size, in bytes, of a symbol is known
as the symbol size.
シンボル: データのユニット。 バイトで表現されるシンボルのサイズはシンボルサイズとして知られています。
Encoding symbol group: a group of encoding symbols that are sent
together, i.e., within the same packet whose relationship to the
source symbols can be derived from a single Encoding Symbol ID.
シンボルをコード化して、分類してください: すなわち、一緒に、そして、単一のEncoding Symbol IDからソースシンボルとの関係を得ることができるのと同じパケットの中で送られるコード化シンボルのグループ。
Encoding Symbol ID: information that defines the relationship
between the symbols of an encoding symbol group and the source
symbols.
Symbol IDをコード化します: シンボルグループをコード化して、ソースシンボルのシンボルの間の関係を定義する情報。
Encoding packet: data packets that contain encoding symbols
パケットをコード化します: コード化シンボルを含むデータ・パケット
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Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[8ページ]。
Sub-block: a source block is sometimes broken into sub-blocks,
each of which is sufficiently small to be decoded in working
memory. For a source block consisting of K source symbols, each
sub-block consists of K sub-symbols, each symbol of the source
block being composed of one sub-symbol from each sub-block.
サブブロック: サブブロックは時々ソースブロックにワーキングメモリで解読されていた状態で細かく分けられます。それはそれぞれであることができる小さいです。 Kソースシンボルから成るソースブロックに関しては、それぞれのサブブロックはKサブシンボル(それぞれのサブブロックから1つのサブシンボルで構成されるソースブロックの各シンボル)から成ります。
Sub-symbol: part of a symbol. Each source symbol is composed of
as many sub-symbols as there are sub-blocks in the source block.
サブシンボル: シンボルの一部。 それぞれのソースシンボルはソースブロックでのサブブロックであるあるのと同じくらい多くのサブシンボルで構成されます。
Source packet: data packets that contain source symbols.
ソースパケット: ソースシンボルを含むデータ・パケット。
Repair packet: data packets that contain repair symbols.
パケットを修理してください: 修理シンボルを含むデータ・パケット。
5.1.2. Symbols
5.1.2. シンボル
i, j, x, h, a, b, d, v, m represent positive integers.
i、j、x、h、a、b、d、v、mは正の整数を表します。
ceil(x) denotes the smallest positive integer that is greater than
or equal to x.
ceil(x)はそう以上である最もわずかな正の整数を指示します。x。
choose(i,j) denotes the number of ways j objects can be chosen from
among i objects without repetition.
(i、j)を選んでください。i物から反復なしで物を選ぶことができる方法jの数を指示します。
floor(x) denotes the largest positive integer that is less than or
equal to x.
床(x)は、よりx以下である最も大きい正の整数を指示します。
i % j denotes i modulo j.
i%jはi法jを指示します。
X ^ Y denotes, for equal-length bit strings X and Y, the bitwise
exclusive-or of X and Y.
X^Yが等しい長さのビット列のためにXとYを指示する、bitwiseする、XとYの排他的論理和。
Al denotes a symbol alignment parameter. Symbol and sub-symbol
sizes are restricted to be multiples of Al.
アルはシンボル整列パラメタを指示します。 シンボルとサブシンボルサイズは、アルの倍数になるように制限されます。
A denotes a matrix over GF(2).
AはGF(2)の上でマトリクスを指示します。
Transpose[A] denotes the transposed matrix of matrix A.
[A]を転移させてください。マトリクスAの転置行列を指示します。
A^^-1 denotes the inverse matrix of matrix A.
^^-1はマトリクスAの逆さのマトリクスを指示します。
K denotes the number of symbols in a single source block.
Kは1つのソースブロックのシンボルの数を指示します。
Kmax denotes the maximum number of source symbols that can be in a
single source block. Set to 8192.
Kmaxは1つのソースブロックにあることができるソースシンボルの最大数を指示します。 8192にセットしてください。
L denotes the number of pre-coding symbols for a single source
block.
Lは1つのソースブロックのプレコード化シンボルの数を指示します。
Luby, et al. Standards Track [Page 9] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[9ページ]。
S denotes the number of LDPC symbols for a single source block.
Sは1つのソースブロックのLDPCシンボルの数を指示します。
H denotes the number of Half symbols for a single source block.
Hは1つのソースブロックのHalfシンボルの数を指示します。
C denotes an array of intermediate symbols, C[0], C[1], C[2],...,
C[L-1].
C[2]、Cは中間的シンボル、C[0]、C[1]の勢ぞろいを指示します…, C[L-1]。
C' denotes an array of source symbols, C'[0], C'[1], C'[2],...,
C'[K-1].
'C'はソースシンボルの勢ぞろい、C'[0]、C'[1]、C'[2]を指示します'…, 'C'[K-1]。
X a non-negative integer value
Xは非負の整数値です。
V0, V1 two arrays of 4-byte integers, V0[0], V0[1],..., V0[255] and
V1[0], V1[1],..., V1[255]
V0、4バイトの整数、V0[0]、V0[1]のV1twoアレイ…, V0[255]とV1[0]、V1[1]…, V1[255]
Rand[X, i, m] a pseudo-random number generator
ランド[X、i、m]は疑似乱数生成器です。
Deg[v] a degree generator
度[v]1度ジェネレータ
LTEnc[K, C ,(d, a, b)] a LT encoding symbol generator
シンボルジェネレータをコード化するLTEnc[K、C(d、a、b)]a LT
Trip[K, X] a triple generator function
旅行[K、X]のa三重のジェネレータ機能
G the number of symbols within an encoding symbol group
コード化シンボルの中のシンボルの数が分類するG
GF(n) the Galois field with n elements.
GF(n)のガロアはnで要素をさばきます。
N the number of sub-blocks within a source block
N ソースブロックの中のサブブロックの数
T the symbol size in bytes. If the source block is partitioned
into sub-blocks, then T = T'*N.
T、バイトで表現されるシンボルサイズ。 'ソースブロックがサブブロックに仕切られるなら、TはT'*Nと等しいです。
T' the sub-symbol size, in bytes. If the source block is not
partitioned into sub-blocks, then T' is not relevant.
'T、'バイトで表現されるサブシンボルサイズ。 'ソースブロックがサブブロックに仕切られないなら、T'は関連していません。
F the transfer length of an object, in bytes
Fはバイトで表現される物の転送の長さです。
I the sub-block size in bytes
私はバイトで表現されるサブブロック・サイズです。
P for object delivery, the payload size of each packet, in bytes,
that is used in the recommended derivation of the object
delivery transport parameters.
物の配送、バイトで表現される物の配送輸送パラメタのお勧めの派生に使用されるそれぞれのパケットのペイロードサイズのためのP。
Q Q = 65521, i.e., Q is the largest prime smaller than 2^^16
すなわち、Q Q=65521、Qは2^^16より小さい最も大きい主要です。
Z the number of source blocks, for object delivery
Zは物の配送のためのソースブロックの数です。
J(K) the systematic index associated with K
系統的が索引をつけるJ(K)はKと交際しました。
Luby, et al. Standards Track [Page 10] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[10ページ]。
I_S denotes the SxS identity matrix.
I_SはSxSアイデンティティマトリクスを指示します。
0_SxH denotes the SxH zero matrix.
0_SxHはSxHゼロ行列を指示します。
a ^^ b a raised to the power b
^^b aはbを巾乗しました。
5.1.3. Abbreviations
5.1.3. 略語
For the purposes of the present document, the following abbreviations apply:
現在のドキュメントの目的のために、以下の略語は申し込まれます:
ESI Encoding Symbol ID
Symbol IDをコード化するESI
LDPC Low Density Parity Check
LDPCの低い密度パリティチェック
LT Luby Transform
LT Lubyは変形します。
SBN Source Block Number
SBNソース街区番号
SBL Source Block Length (in units of symbols)
SBLソースブロック長(ユニットのシンボルの)
5.2. Overview
5.2. 概観
The principal component of the systematic Raptor code is the basic encoder described in Section 5.4. First, it is described how to derive values for a set of intermediate symbols from the original source symbols such that knowledge of the intermediate symbols is sufficient to reconstruct the source symbols. Secondly, the encoder produces repair symbols, which are each the exclusive OR of a number of the intermediate symbols. The encoding symbols are the combination of the source and repair symbols. The repair symbols are produced in such a way that the intermediate symbols, and therefore also the source symbols, can be recovered from any sufficiently large set of encoding symbols.
系統的なRaptorコードの主成分はセクション5.4で説明された基本的なエンコーダです。 まず最初に1セットの中間的シンボルのために一次資料シンボルから値をどのように引き出すかが説明されるので、中間的シンボルに関する知識はソースシンボルを再建するために十分です。 第二に、エンコーダは修理シンボルを作成します。(シンボルはaの排他的論理和が付番する中間的シンボルのそれぞれです)。 コード化シンボルはソースと修理シンボルの組み合わせです。 修理シンボルはどんな十分大きいセットについてもシンボルをコード化するのを中間的シンボル、およびしたがって、ソースシンボルからも取り戻すことができるような方法で作成されます。
This document specifies the systematic Raptor code encoder. A number of possible decoding algorithms are possible. An efficient decoding algorithm is provided in Section 5.5.
このドキュメントは系統的なRaptorコードエンコーダを指定します。 多くの可能な解読アルゴリズムが可能です。 効率的な解読アルゴリズムをセクション5.5に提供します。
The construction of the intermediate and repair symbols is based in part on a pseudo-random number generator described in Section 5.4.4.1. This generator is based on a fixed set of 512 random numbers that MUST be available to both sender and receiver. These are provided in Section 5.6.
中間介在物と修理シンボルの工事はセクション5.4.4で.1に説明された疑似乱数生成器に一部基づいています。 このジェネレータを送付者と受信機の両方に利用可能であるに違いない512の乱数の固定セットに基礎づけます。セクション5.6にこれらを提供します。
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Finally, the construction of the intermediate symbols from the source symbols is governed by a 'systematic index', values of which are provided in Section 5.7 for source block sizes from 4 source symbols to Kmax = 8192 source symbols.
最終的に、ソースシンボルからの中間的シンボルの工事は'系統的なインデックス'によって治められます。その値はソースブロック・サイズのために4つのソースシンボルから8192のソースKmax=シンボルまでセクション5.7に提供されます。
5.3. Object Delivery
5.3. 物の配送
5.3.1. Source Block Construction
5.3.1. ソースブロック工事
5.3.1.1. General
5.3.1.1. 一般
In order to apply the Raptor encoder to a source object, the object may be broken into Z >= 1 blocks, known as source blocks. The Raptor encoder is applied independently to each source block. Each source block is identified by a unique integer Source Block Number (SBN), where the first source block has SBN zero, the second has SBN one, etc. Each source block is divided into a number, K, of source symbols of size T bytes each. Each source symbol is identified by a unique integer Encoding Symbol Identifier (ESI), where the first source symbol of a source block has ESI zero, the second has ESI one, etc.
Raptorエンコーダをソース物に適用するために、1が妨げるZ>=は物に細かく分けられるかもしれません、ソースブロックとして知られていて。 Raptorエンコーダは独自にそれぞれのソースブロックに適用されます。 それぞれのソースブロックはユニークな整数Source Block Number(SBN)によって特定されます。そこでは、最初のソースブロックにはSBNゼロがあって、2番目はSBN1などを持っています。 それぞれのソースブロックは数、それぞれサイズTバイトのソースシンボルのKに分割されます。 それぞれのソースシンボルはユニークな整数Encoding Symbol Identifier(ESI)によって特定されます。そこでは、1つのソースブロックの最初のソースシンボルにはESIゼロがあって、2番目はESI1などを持っています。
Each source block with K source symbols is divided into N >= 1 sub- blocks, which are small enough to be decoded in the working memory. Each sub-block is divided into K sub-symbols of size T'.
KソースシンボルがあるそれぞれのソースブロックはN>=1にサブブロックする状態で分割されます(ワーキングメモリで解読できるくらい小さいです)。 'それぞれのサブブロックはサイズTのKサブシンボルに分割されます'。
Note that the value of K is not necessarily the same for each source block of an object and the value of T' may not necessarily be the same for each sub-block of a source block. However, the symbol size T is the same for all source blocks of an object and the number of symbols, K, is the same for every sub-block of a source block. Exact partitioning of the object into source blocks and sub-blocks is described in Section 5.3.1.2 below.
'物のそれぞれのソースブロックには、Kの値が必ず同じであるというわけではなく、1つのソースブロックのそれぞれのサブブロックには、T'の値が必ず同じであるかもしれないというわけではないことに注意してください。 しかしながら、物のすべてのソースブロックに、シンボルサイズTは同じです、そして、1つのソースブロックのあらゆるサブブロックに、シンボルの数(K)は同じです。 物の正確な仕切りはセクション5.3でソースブロックとサブブロックに説明されます。
5.3.1.2. Source Block and Sub-Block Partitioning
5.3.1.2. ソースブロックとサブブロック仕切り
The construction of source blocks and sub-blocks is determined based on five input parameters, F, Al, T, Z, and N, and a function Partition[]. The five input parameters are defined as follows:
ソースブロックとサブブロックの構造は5つの入力パラメタ、F、アル、T、Z、N、および機能Partition[]に基づいて決定しています。 5つの入力パラメタが以下の通り定義されます:
- F the transfer length of the object, in bytes
- Fはバイトで表現される物の転送の長さです。
- Al a symbol alignment parameter, in bytes
- アルはバイトで表現されるシンボル整列パラメタです。
- T the symbol size, in bytes, which MUST be a multiple of Al
- Tはアルの倍数であるに違いないバイトで表現されるシンボルサイズです。
- Z the number of source blocks
- Zはソースブロックの数です。
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- N the number of sub-blocks in each source block
- N それぞれのソースブロックのサブブロックの数
These parameters MUST be set so that ceil(ceil(F/T)/Z) <= Kmax. Recommendations for derivation of these parameters are provided in Section 4.2.
これらのパラメタを設定しなければならないので、ceil(ceil(F/T)/Z)<はKmaxと等しいです。 これらのパラメタの派生のための推薦をセクション4.2に提供します。
The function Partition[] takes a pair of integers (I, J) as input and derives four integers (IL, IS, JL, JS) as output. Specifically, the value of Partition[I, J] is a sequence of four integers (IL, IS, JL, JS), where IL = ceil(I/J), IS = floor(I/J), JL = I - IS * J, and JS = J - JL. Partition[] derives parameters for partitioning a block of size I into J approximately equal-sized blocks. Specifically, JL blocks of length IL and JS blocks of length IS.
機能Partition[]が入力されるように1組の整数(I、J)を取って、4つの整数を引き出す、(IL、ある、JL、JS) 出力されるように。 明確に、Partition[I、J]の値が4つの整数の系列である、(IL、ある、JL、JS) JLは私と等しいです--JSはJと等しいです--=はILがceil(I/J)と等しいところでは、床(I/J)です、そして、*がJです、そして、JL。 パーティション[]はサイズIのJへのブロックでほとんど等しいサイズのブロックを仕切るためのパラメタを引き出します。 明確に、JLブロックの長さのILとJSブロックの長さはそうです。
The source object MUST be partitioned into source blocks and sub- blocks as follows:
The source object MUST be partitioned into source blocks and sub- blocks as follows:
Let
Let
Kt = ceil(F/T)
Kt = ceil(F/T)
(KL, KS, ZL, ZS) = Partition[Kt, Z]
(KL, KS, ZL, ZS) = Partition[Kt, Z]
(TL, TS, NL, NS) = Partition[T/Al, N]
(TL, TS, NL, NS) = Partition[T/Al, N]
Then, the object MUST be partitioned into Z = ZL + ZS contiguous source blocks, the first ZL source blocks each having length KL*T bytes, and the remaining ZS source blocks each having KS*T bytes.
Then, the object MUST be partitioned into Z = ZL + ZS contiguous source blocks, the first ZL source blocks each having length KL*T bytes, and the remaining ZS source blocks each having KS*T bytes.
If Kt*T > F, then for encoding purposes, the last symbol MUST be padded at the end with Kt*T - F zero bytes.
If Kt*T > F, then for encoding purposes, the last symbol MUST be padded at the end with Kt*T - F zero bytes.
Next, each source block MUST be divided into N = NL + NS contiguous sub-blocks, the first NL sub-blocks each consisting of K contiguous sub-symbols of size of TL*Al and the remaining NS sub-blocks each consisting of K contiguous sub-symbols of size of TS*Al. The symbol alignment parameter Al ensures that sub-symbols are always a multiple of Al bytes.
Next, each source block MUST be divided into N = NL + NS contiguous sub-blocks, the first NL sub-blocks each consisting of K contiguous sub-symbols of size of TL*Al and the remaining NS sub-blocks each consisting of K contiguous sub-symbols of size of TS*Al. The symbol alignment parameter Al ensures that sub-symbols are always a multiple of Al bytes.
Finally, the m-th symbol of a source block consists of the concatenation of the m-th sub-symbol from each of the N sub-blocks. Note that this implies that when N > 1, then a symbol is NOT a contiguous portion of the object.
Finally, the m-th symbol of a source block consists of the concatenation of the m-th sub-symbol from each of the N sub-blocks. Note that this implies that when N > 1, then a symbol is NOT a contiguous portion of the object.
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Luby, et al. Standards Track [Page 13] RFC 5053 Raptor FEC Scheme October 2007
5.3.2. Encoding Packet Construction
5.3.2. Encoding Packet Construction
Each encoding packet contains the following information:
Each encoding packet contains the following information:
- Source Block Number (SBN)
- Source Block Number (SBN)
- Encoding Symbol ID (ESI)
- Encoding Symbol ID (ESI)
- encoding symbol(s)
- encoding symbol(s)
Each source block is encoded independently of the others. Source blocks are numbered consecutively from zero.
Each source block is encoded independently of the others. Source blocks are numbered consecutively from zero.
Encoding Symbol ID values from 0 to K-1 identify the source symbols of a source block in sequential order, where K is the number of symbols in the source block. Encoding Symbol IDs from K onwards identify repair symbols.
Encoding Symbol ID values from 0 to K-1 identify the source symbols of a source block in sequential order, where K is the number of symbols in the source block. Encoding Symbol IDs from K onwards identify repair symbols.
Each encoding packet either consists entirely of source symbols (source packet) or entirely of repair symbols (repair packet). A packet may contain any number of symbols from the same source block. In the case that the last source symbol in a source packet includes padding bytes added for FEC encoding purposes, then these bytes need not be included in the packet. Otherwise, only whole symbols MUST be included.
Each encoding packet either consists entirely of source symbols (source packet) or entirely of repair symbols (repair packet). A packet may contain any number of symbols from the same source block. In the case that the last source symbol in a source packet includes padding bytes added for FEC encoding purposes, then these bytes need not be included in the packet. Otherwise, only whole symbols MUST be included.
The Encoding Symbol ID, X, carried in each source packet is the Encoding Symbol ID of the first source symbol carried in that packet. The subsequent source symbols in the packet have Encoding Symbol IDs, X+1 to X+G-1, in sequential order, where G is the number of symbols in the packet.
The Encoding Symbol ID, X, carried in each source packet is the Encoding Symbol ID of the first source symbol carried in that packet. The subsequent source symbols in the packet have Encoding Symbol IDs, X+1 to X+G-1, in sequential order, where G is the number of symbols in the packet.
Similarly, the Encoding Symbol ID, X, placed into a repair packet is the Encoding Symbol ID of the first repair symbol in the repair packet and the subsequent repair symbols in the packet have Encoding Symbol IDs X+1 to X+G-1 in sequential order, where G is the number of symbols in the packet.
Similarly, the Encoding Symbol ID, X, placed into a repair packet is the Encoding Symbol ID of the first repair symbol in the repair packet and the subsequent repair symbols in the packet have Encoding Symbol IDs X+1 to X+G-1 in sequential order, where G is the number of symbols in the packet.
Note that it is not necessary for the receiver to know the total number of repair packets.
Note that it is not necessary for the receiver to know the total number of repair packets.
Associated with each symbol is a triple of integers (d, a, b).
Associated with each symbol is a triple of integers (d, a, b).
The G repair symbol triples (d[0], a[0], b[0]),..., (d[G-1], a[G-1], b[G-1]) for the repair symbols placed into a repair packet with ESI X are computed using the Triple generator defined in Section 5.4.4.4 as follows:
The G repair symbol triples (d[0], a[0], b[0]),..., (d[G-1], a[G-1], b[G-1]) for the repair symbols placed into a repair packet with ESI X are computed using the Triple generator defined in Section 5.4.4.4 as follows:
Luby, et al. Standards Track [Page 14] RFC 5053 Raptor FEC Scheme October 2007
Luby, et al. Standards Track [Page 14] RFC 5053 Raptor FEC Scheme October 2007
For each i = 0, ..., G-1, (d[i], a[i], b[i]) = Trip[K,X+i]
For each i = 0, ..., G-1, (d[i], a[i], b[i]) = Trip[K,X+i]
The G repair symbols to be placed in repair packet with ESI X are calculated based on the repair symbol triples, as described in Section 5.4, using the intermediate symbols C and the LT encoder LTEnc[K, C, (d[i], a[i], b[i])].
The G repair symbols to be placed in repair packet with ESI X are calculated based on the repair symbol triples, as described in Section 5.4, using the intermediate symbols C and the LT encoder LTEnc[K, C, (d[i], a[i], b[i])].
5.4. Systematic Raptor Encoder
5.4. Systematic Raptor Encoder
5.4.1. Encoding Overview
5.4.1. Encoding Overview
The systematic Raptor encoder is used to generate repair symbols from a source block that consists of K source symbols.
The systematic Raptor encoder is used to generate repair symbols from a source block that consists of K source symbols.
Symbols are the fundamental data units of the encoding and decoding process. For each source block (sub-block), all symbols (sub- symbols) are the same size. The atomic operation performed on symbols (sub-symbols) for both encoding and decoding is the exclusive-or operation.
Symbols are the fundamental data units of the encoding and decoding process. For each source block (sub-block), all symbols (sub- symbols) are the same size. The atomic operation performed on symbols (sub-symbols) for both encoding and decoding is the exclusive-or operation.
Let C'[0],..., C'[K-1] denote the K source symbols.
Let C'[0],..., C'[K-1] denote the K source symbols.
Let C[0],..., C[L-1] denote L intermediate symbols.
Let C[0],..., C[L-1] denote L intermediate symbols.
The first step of encoding is to generate a number, L > K, of intermediate symbols from the K source symbols. In this step, K source symbol triples (d[0], a[0], b[0]), ..., (d[K-1], a[K-1], b[K-1]) are generated using the Trip[] generator as described in Section 5.4.2.2. The K source symbol triples are associated with the K source symbols and are then used to determine the L intermediate symbols C[0],..., C[L-1] from the source symbols using an inverse encoding process. This process can be realized by a Raptor decoding process.
The first step of encoding is to generate a number, L > K, of intermediate symbols from the K source symbols. In this step, K source symbol triples (d[0], a[0], b[0]), ..., (d[K-1], a[K-1], b[K-1]) are generated using the Trip[] generator as described in Section 5.4.2.2. The K source symbol triples are associated with the K source symbols and are then used to determine the L intermediate symbols C[0],..., C[L-1] from the source symbols using an inverse encoding process. This process can be realized by a Raptor decoding process.
Certain "pre-coding relationships" MUST hold within the L intermediate symbols. Section 5.4.2.3 describes these relationships and how the intermediate symbols are generated from the source symbols.
Certain "pre-coding relationships" MUST hold within the L intermediate symbols. Section 5.4.2.3 describes these relationships and how the intermediate symbols are generated from the source symbols.
Once the intermediate symbols have been generated, repair symbols are produced and one or more repair symbols are placed as a group into a single data packet. Each repair symbol group is associated with an Encoding Symbol ID (ESI) and a number, G, of repair symbols. The ESI is used to generate a triple of three integers, (d, a, b) for each repair symbol, again using the Trip[] generator as described in Section 5.4.4.4. Then, each (d,a,b)-triple is used to generate the
Once the intermediate symbols have been generated, repair symbols are produced and one or more repair symbols are placed as a group into a single data packet. Each repair symbol group is associated with an Encoding Symbol ID (ESI) and a number, G, of repair symbols. The ESI is used to generate a triple of three integers, (d, a, b) for each repair symbol, again using the Trip[] generator as described in Section 5.4.4.4. Then, each (d,a,b)-triple is used to generate the
Luby, et al. Standards Track [Page 15] RFC 5053 Raptor FEC Scheme October 2007
Luby, et al. Standards Track [Page 15] RFC 5053 Raptor FEC Scheme October 2007
corresponding repair symbol from the intermediate symbols using the LTEnc[K, C[0],..., C[L-1], (d,a,b)] generator described in Section 5.4.4.3.
corresponding repair symbol from the intermediate symbols using the LTEnc[K, C[0],..., C[L-1], (d,a,b)] generator described in Section 5.4.4.3.
5.4.2. First Encoding Step: Intermediate Symbol Generation
5.4.2. First Encoding Step: Intermediate Symbol Generation
5.4.2.1. General
5.4.2.1. General
The first encoding step is a pre-coding step to generate the L intermediate symbols C[0], ..., C[L-1] from the source symbols C'[0], ..., C'[K-1]. The intermediate symbols are uniquely defined by two sets of constraints:
The first encoding step is a pre-coding step to generate the L intermediate symbols C[0], ..., C[L-1] from the source symbols C'[0], ..., C'[K-1]. The intermediate symbols are uniquely defined by two sets of constraints:
1. The intermediate symbols are related to the source symbols by
a set of source symbol triples. The generation of the source
symbol triples is defined in Section 5.4.2.2 using the Trip[]
generator described in Section 5.4.4.4.
1. The intermediate symbols are related to the source symbols by a set of source symbol triples. The generation of the source symbol triples is defined in Section 5.4.2.2 using the Trip[] generator described in Section 5.4.4.4.
2. A set of pre-coding relationships hold within the intermediate
symbols themselves. These are defined in Section 5.4.2.3.
2. A set of pre-coding relationships hold within the intermediate symbols themselves. These are defined in Section 5.4.2.3.
The generation of the L intermediate symbols is then defined in Section 5.4.2.4
The generation of the L intermediate symbols is then defined in Section 5.4.2.4
5.4.2.2. Source Symbol Triples
5.4.2.2. Source Symbol Triples
Each of the K source symbols is associated with a triple (d[i], a[i], b[i]) for 0 <= i < K. The source symbol triples are determined using the Triple generator defined in Section 5.4.4.4 as:
Each of the K source symbols is associated with a triple (d[i], a[i], b[i]) for 0 <= i < K. The source symbol triples are determined using the Triple generator defined in Section 5.4.4.4 as:
For each i, 0 <= i < K
For each i, 0 <= i < K
(d[i], a[i], b[i]) = Trip[K, i]
(d[i], a[i], b[i]) = Trip[K, i]
5.4.2.3. Pre-Coding Relationships
5.4.2.3. Pre-Coding Relationships
The pre-coding relationships amongst the L intermediate symbols are defined by expressing the last L-K intermediate symbols in terms of the first K intermediate symbols.
The pre-coding relationships amongst the L intermediate symbols are defined by expressing the last L-K intermediate symbols in terms of the first K intermediate symbols.
The last L-K intermediate symbols C[K],...,C[L-1] consist of S LDPC symbols and H Half symbols The values of S and H are determined from K as described below. Then L = K+S+H.
The last L-K intermediate symbols C[K],...,C[L-1] consist of S LDPC symbols and H Half symbols The values of S and H are determined from K as described below. Then L = K+S+H.
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Luby, et al. Standards Track [Page 16] RFC 5053 Raptor FEC Scheme October 2007
Let
Let
X be the smallest positive integer such that X*(X-1) >= 2*K.
X be the smallest positive integer such that X*(X-1) >= 2*K.
S be the smallest prime integer such that S >= ceil(0.01*K) + X
S be the smallest prime integer such that S >= ceil(0.01*K) + X
H be the smallest integer such that choose(H,ceil(H/2)) >= K + S
H be the smallest integer such that choose(H,ceil(H/2)) >= K + S
H' = ceil(H/2)
H' = ceil(H/2)
L = K+S+H
L = K+S+H
C[0],...,C[K-1] denote the first K intermediate symbols
C[0],...,C[K-1] denote the first K intermediate symbols
C[K],...,C[K+S-1] denote the S LDPC symbols, initialised to zero
C[K],...,C[K+S-1] denote the S LDPC symbols, initialised to zero
C[K+S],...,C[L-1] denote the H Half symbols, initialised to zero
C[K+S],...,C[L-1] denote the H Half symbols, initialised to zero
The S LDPC symbols are defined to be the values of C[K],...,C[K+S-1] at the end of the following process:
The S LDPC symbols are defined to be the values of C[K],...,C[K+S-1] at the end of the following process:
For i = 0,...,K-1 do
For i = 0,...,K-1 do
a = 1 + (floor(i/S) % (S-1))
a = 1 + (floor(i/S) % (S-1))
b = i % S
b = i % S
C[K + b] = C[K + b] ^ C[i]
C[K + b] = C[K + b] ^ C[i]
b = (b + a) % S
b = (b + a) % S
C[K + b] = C[K + b] ^ C[i]
C[K + b] = C[K + b] ^ C[i]
b = (b + a) % S
b = (b + a) % S
C[K + b] = C[K + b] ^ C[i]
C[K + b] = C[K + b] ^ C[i]
The H Half symbols are defined as follows:
The H Half symbols are defined as follows:
Let
Let
g[i] = i ^ (floor(i/2)) for all positive integers i
g[i] = i ^ (floor(i/2)) for all positive integers i
Note: g[i] is the Gray sequence, in which each element differs
from the previous one in a single bit position
Note: g[i] is the Gray sequence, in which each element differs from the previous one in a single bit position
m[k] denote the subsequence of g[.] whose elements have exactly k
non-zero bits in their binary representation.
m[k] denote the subsequence of g[.] whose elements have exactly k non-zero bits in their binary representation.
Luby, et al. Standards Track [Page 17] RFC 5053 Raptor FEC Scheme October 2007
Luby, et al. Standards Track [Page 17] RFC 5053 Raptor FEC Scheme October 2007
m[j,k] denote the jth element of the sequence m[k], where j=0, 1,
2, ...
m[j,k] denote the jth element of the sequence m[k], where j=0, 1, 2, ...
Then, the Half symbols are defined as the values of C[K+S],...,C[L-1] after the following process:
Then, the Half symbols are defined as the values of C[K+S],...,C[L-1] after the following process:
For h = 0,...,H-1 do
For h = 0,...,H-1 do
For j = 0,...,K+S-1 do
For j = 0,...,K+S-1 do
If bit h of m[j,H'] is equal to 1 then C[h+K+S] = C[h+K+S] ^
C[j].
If bit h of m[j,H'] is equal to 1 then C[h+K+S] = C[h+K+S] ^ C[j].
5.4.2.4. Intermediate Symbols
5.4.2.4. Intermediate Symbols
5.4.2.4.1. Definition
5.4.2.4.1. Definition
Given the K source symbols C'[0], C'[1],..., C'[K-1] the L intermediate symbols C[0], C[1],..., C[L-1] are the uniquely defined symbol values that satisfy the following conditions:
Given the K source symbols C'[0], C'[1],..., C'[K-1] the L intermediate symbols C[0], C[1],..., C[L-1] are the uniquely defined symbol values that satisfy the following conditions:
1. The K source symbols C'[0], C'[1],..., C'[K-1] satisfy the K
constraints
1. The K source symbols C'[0], C'[1],..., C'[K-1] satisfy the K constraints
C'[i] = LTEnc[K, (C[0],..., C[L-1]), (d[i], a[i], b[i])], for
all i, 0 <= i < K.
C'[i] = LTEnc[K, (C[0],..., C[L-1]), (d[i], a[i], b[i])], for all i, 0 <= i < K.
2. The L intermediate symbols C[0], C[1],..., C[L-1] satisfy the
pre-coding relationships defined in Section 5.4.2.3.
2. The L intermediate symbols C[0], C[1],..., C[L-1] satisfy the pre-coding relationships defined in Section 5.4.2.3.
5.4.2.4.2. Example Method for Calculation of Intermediate Symbols
5.4.2.4.2. Example Method for Calculation of Intermediate Symbols
This subsection describes a possible method for calculation of the L intermediate symbols C[0], C[1],..., C[L-1] satisfying the constraints in Section 5.4.2.4.1.
This subsection describes a possible method for calculation of the L intermediate symbols C[0], C[1],..., C[L-1] satisfying the constraints in Section 5.4.2.4.1.
The 'generator matrix' for a code that generates N output symbols from K input symbols is an NxK matrix over GF(2), where each row corresponds to one of the output symbols and each column to one of the input symbols and where the ith output symbol is equal to the sum of those input symbols whose column contains a non-zero entry in row i.
The 'generator matrix' for a code that generates N output symbols from K input symbols is an NxK matrix over GF(2), where each row corresponds to one of the output symbols and each column to one of the input symbols and where the ith output symbol is equal to the sum of those input symbols whose column contains a non-zero entry in row i.
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Luby, et al. Standards Track [Page 18] RFC 5053 Raptor FEC Scheme October 2007
Then, the L intermediate symbols can be calculated as follows:
Then, the L intermediate symbols can be calculated as follows:
Let
Let
C denote the column vector of the L intermediate symbols, C[0],
C[1],..., C[L-1].
C denote the column vector of the L intermediate symbols, C[0], C[1],..., C[L-1].
D denote the column vector consisting of S+H zero symbols followed
by the K source symbols C'[0], C'[1], ..., C'[K-1]
D denote the column vector consisting of S+H zero symbols followed by the K source symbols C'[0], C'[1], ..., C'[K-1]
Then the above constraints define an LxL matrix over GF(2), A, such that:
Then the above constraints define an LxL matrix over GF(2), A, such that:
A*C = D
A*C = D
The matrix A can be constructed as follows:
The matrix A can be constructed as follows:
Let:
Let:
G_LDPC be the S x K generator matrix of the LDPC symbols. So,
G_LDPC be the S x K generator matrix of the LDPC symbols. So,
G_LDPC * Transpose[(C[0],...., C[K-1])] = Transpose[(C[K], ...,
C[K+S-1])]
G_LDPC * Transpose[(C[0],...., C[K-1])] = Transpose[(C[K], ..., C[K+S-1])]
G_Half be the H x (K+S) generator matrix of the Half symbols, So,
G_Half be the H x (K+S) generator matrix of the Half symbols, So,
G_Half * Transpose[(C[0], ..., C[S+K-1])] = Transpose[(C[K+S],
..., C[K+S+H-1])]
G_Half * Transpose[(C[0], ..., C[S+K-1])] = Transpose[(C[K+S], ..., C[K+S+H-1])]
I_S be the S x S identity matrix
I_S be the S x S identity matrix
I_H be the H x H identity matrix
I_H be the H x H identity matrix
0_SxH be the S x H zero matrix
0_SxH be the S x H zero matrix
G_LT be the KxL generator matrix of the encoding symbols generated
by the LT Encoder. So,
G_LT be the KxL generator matrix of the encoding symbols generated by the LT Encoder. So,
G_LT * Transpose[(C[0], ..., C[L-1])] =
Transpose[(C'[0],C'[1],...,C'[K-1])]
G_LT * Transpose[(C[0], ..., C[L-1])] = Transpose[(C'[0],C'[1],...,C'[K-1])]
i.e., G_LT(i,j) = 1 if and only if C[j] is included in the
symbols that are XORed to produce LTEnc[K, (C[0], ..., C[L-1]),
(d[i], a[i], b[i])].
i.e., G_LT(i,j) = 1 if and only if C[j] is included in the symbols that are XORed to produce LTEnc[K, (C[0], ..., C[L-1]), (d[i], a[i], b[i])].
Then:
Then:
The first S rows of A are equal to G_LDPC | I_S | 0_SxH.
The first S rows of A are equal to G_LDPC | I_S | 0_SxH.
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Luby, et al. Standards Track [Page 19] RFC 5053 Raptor FEC Scheme October 2007
The next H rows of A are equal to G_Half | I_H.
The next H rows of A are equal to G_Half | I_H.
The remaining K rows of A are equal to G_LT.
The remaining K rows of A are equal to G_LT.
The matrix A is depicted in Figure 4 below:
The matrix A is depicted in Figure 4 below:
K S H
+-----------------------+-------+-------+
| | | |
S | G_LDPC | I_S | 0_SxH |
| | | |
+-----------------------+-------+-------+
| | |
H | G_Half | I_H |
| | |
+-------------------------------+-------+
| |
| |
K | G_LT |
| |
| |
+---------------------------------------+
K S H +-----------------------+-------+-------+ | | | | S | G_LDPC | I_S | 0_SxH | | | | | +-----------------------+-------+-------+ | | | H | G_Half | I_H | | | | +-------------------------------+-------+ | | | | K | G_LT | | | | | +---------------------------------------+
Figure 4: The matrix A
Figure 4: The matrix A
The intermediate symbols can then be calculated as:
The intermediate symbols can then be calculated as:
C = (A^^-1)*D
C = (A^^-1)*D
The source symbol triples are generated such that for any K matrix, A has full rank and is therefore invertible. This calculation can be realized by applying a Raptor decoding process to the K source symbols C'[0], C'[1],..., C'[K-1] to produce the L intermediate symbols C[0], C[1],..., C[L-1].
The source symbol triples are generated such that for any K matrix, A has full rank and is therefore invertible. This calculation can be realized by applying a Raptor decoding process to the K source symbols C'[0], C'[1],..., C'[K-1] to produce the L intermediate symbols C[0], C[1],..., C[L-1].
To efficiently generate the intermediate symbols from the source symbols, it is recommended that an efficient decoder implementation such as that described in Section 5.5 be used. The source symbol triples are designed to facilitate efficient decoding of the source symbols using that algorithm.
To efficiently generate the intermediate symbols from the source symbols, it is recommended that an efficient decoder implementation such as that described in Section 5.5 be used. The source symbol triples are designed to facilitate efficient decoding of the source symbols using that algorithm.
5.4.3. Second Encoding Step: LT Encoding
5.4.3. Second Encoding Step: LT Encoding
In the second encoding step, the repair symbol with ESI X is generated by applying the generator LTEnc[K, (C[0], C[1],..., C[L-1]), (d, a, b)] defined in Section 5.4.4.3 to the L intermediate symbols C[0], C[1],..., C[L-1] using the triple (d, a, b)=Trip[K,X] generated according to Section 5.3.2
In the second encoding step, the repair symbol with ESI X is generated by applying the generator LTEnc[K, (C[0], C[1],..., C[L-1]), (d, a, b)] defined in Section 5.4.4.3 to the L intermediate symbols C[0], C[1],..., C[L-1] using the triple (d, a, b)=Trip[K,X] generated according to Section 5.3.2
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Luby, et al. Standards Track [Page 20] RFC 5053 Raptor FEC Scheme October 2007
5.4.4. Generators
5.4.4. Generators
5.4.4.1. Random Generator
5.4.4.1. Random Generator
The random number generator Rand[X, i, m] is defined as follows, where X is a non-negative integer, i is a non-negative integer, and m is a positive integer and the value produced is an integer between 0 and m-1. Let V0 and V1 be arrays of 256 entries each, where each entry is a 4-byte unsigned integer. These arrays are provided in Section 5.6.
The random number generator Rand[X, i, m] is defined as follows, where X is a non-negative integer, i is a non-negative integer, and m is a positive integer and the value produced is an integer between 0 and m-1. Let V0 and V1 be arrays of 256 entries each, where each entry is a 4-byte unsigned integer. These arrays are provided in Section 5.6.
Then,
Then,
Rand[X, i, m] = (V0[(X + i) % 256] ^ V1[(floor(X/256)+ i) % 256])
% m
Rand[X, i, m] = (V0[(X + i) % 256] ^ V1[(floor(X/256)+ i) % 256]) % m
5.4.4.2. Degree Generator
5.4.4.2. Degree Generator
The degree generator Deg[v] is defined as follows, where v is an integer that is at least 0 and less than 2^^20 = 1048576.
The degree generator Deg[v] is defined as follows, where v is an integer that is at least 0 and less than 2^^20 = 1048576.
In Table 1, find the index j such that f[j-1] <= v < f[j]
In Table 1, find the index j such that f[j-1] <= v < f[j]
Then, Deg[v] = d[j]
Then, Deg[v] = d[j]
+---------+---------+------+
| Index j | f[j] | d[j] |
+---------+---------+------+
| 0 | 0 | -- |
| 1 | 10241 | 1 |
| 2 | 491582 | 2 |
| 3 | 712794 | 3 |
| 4 | 831695 | 4 |
| 5 | 948446 | 10 |
| 6 | 1032189 | 11 |
| 7 | 1048576 | 40 |
+---------+---------+------+
+---------+---------+------+ | Index j | f[j] | d[j] | +---------+---------+------+ | 0 | 0 | -- | | 1 | 10241 | 1 | | 2 | 491582 | 2 | | 3 | 712794 | 3 | | 4 | 831695 | 4 | | 5 | 948446 | 10 | | 6 | 1032189 | 11 | | 7 | 1048576 | 40 | +---------+---------+------+
Table 1: Defines the degree distribution for encoding symbols
Table 1: Defines the degree distribution for encoding symbols
5.4.4.3. LT Encoding Symbol Generator
5.4.4.3. LT Encoding Symbol Generator
The encoding symbol generator LTEnc[K, (C[0], C[1],..., C[L-1]), (d, a, b)] takes the following inputs:
The encoding symbol generator LTEnc[K, (C[0], C[1],..., C[L-1]), (d, a, b)] takes the following inputs:
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Luby, et al. Standards Track [Page 21] RFC 5053 Raptor FEC Scheme October 2007
K is the number of source symbols (or sub-symbols) for the source
block (sub-block). Let L be derived from K as described in
Section 5.4.2.3, and let L' be the smallest prime integer greater
than or equal to L.
K is the number of source symbols (or sub-symbols) for the source block (sub-block). Let L be derived from K as described in Section 5.4.2.3, and let L' be the smallest prime integer greater than or equal to L.
(C[0], C[1],..., C[L-1]) is the array of L intermediate symbols
(sub-symbols) generated as described in Section 5.4.2.4.
(C[0], C[1],..., C[L-1]) is the array of L intermediate symbols (sub-symbols) generated as described in Section 5.4.2.4.
(d, a, b) is a source triple determined using the Triple generator
defined in Section 5.4.4.4, whereby
(d, a, b) is a source triple determined using the Triple generator defined in Section 5.4.4.4, whereby
d is an integer denoting an encoding symbol degree
d is an integer denoting an encoding symbol degree
a is an integer between 1 and L'-1 inclusive
a is an integer between 1 and L'-1 inclusive
b is an integer between 0 and L'-1 inclusive
b is an integer between 0 and L'-1 inclusive
The encoding symbol generator produces a single encoding symbol as output, according to the following algorithm:
The encoding symbol generator produces a single encoding symbol as output, according to the following algorithm:
While (b >= L) do b = (b + a) % L'
While (b >= L) do b = (b + a) % L'
Let result = C[b].
Let result = C[b].
For j = 1,...,min(d-1,L-1) do
For j = 1,...,min(d-1,L-1) do
b = (b + a) % L'
b = (b + a) % L'
While (b >= L) do b = (b + a) % L'
While (b >= L) do b = (b + a) % L'
result = result ^ C[b]
result = result ^ C[b]
Return result
Return result
5.4.4.4. Triple Generator
5.4.4.4. Triple Generator
The triple generator Trip[K,X] takes the following inputs:
The triple generator Trip[K,X] takes the following inputs:
K - The number of source symbols
K - The number of source symbols
X - An encoding symbol ID
X - An encoding symbol ID
Let
Let
L be determined from K as described in Section 5.4.2.3
L be determined from K as described in Section 5.4.2.3
L' be the smallest prime that is greater than or equal to L
L' be the smallest prime that is greater than or equal to L
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Luby, et al. Standards Track [Page 22] RFC 5053 Raptor FEC Scheme October 2007
Q = 65521, the largest prime smaller than 2^^16.
Q = 65521, the largest prime smaller than 2^^16.
J(K) be the systematic index associated with K, as defined in
Section 5.7.
J(K) be the systematic index associated with K, as defined in Section 5.7.
The output of the triple generator is a triple, (d, a, b) determined as follows:
The output of the triple generator is a triple, (d, a, b) determined as follows:
A = (53591 + J(K)*997) % Q
A = (53591 + J(K)*997) % Q
B = 10267*(J(K)+1) % Q
B = 10267*(J(K)+1) % Q
Y = (B + X*A) % Q
Y = (B + X*A) % Q
v = Rand[Y, 0, 2^^20]
v = Rand[Y, 0, 2^^20]
d = Deg[v]
d = Deg[v]
a = 1 + Rand[Y, 1, L'-1]
a = 1 + Rand[Y, 1, L'-1]
b = Rand[Y, 2, L']
b = Rand[Y, 2, L']
5.5. Example FEC Decoder
5.5. Example FEC Decoder
5.5.1. General
5.5.1. General
This section describes an efficient decoding algorithm for the Raptor codes described in this specification. Note that each received encoding symbol can be considered as the value of an equation amongst the intermediate symbols. From these simultaneous equations, and the known pre-coding relationships amongst the intermediate symbols, any algorithm for solving simultaneous equations can successfully decode the intermediate symbols and hence the source symbols. However, the algorithm chosen has a major effect on the computational efficiency of the decoding.
This section describes an efficient decoding algorithm for the Raptor codes described in this specification. Note that each received encoding symbol can be considered as the value of an equation amongst the intermediate symbols. From these simultaneous equations, and the known pre-coding relationships amongst the intermediate symbols, any algorithm for solving simultaneous equations can successfully decode the intermediate symbols and hence the source symbols. However, the algorithm chosen has a major effect on the computational efficiency of the decoding.
5.5.2. Decoding a Source Block
5.5.2. Decoding a Source Block
5.5.2.1. General
5.5.2.1. General
It is assumed that the decoder knows the structure of the source block it is to decode, including the symbol size, T, and the number K of symbols in the source block.
It is assumed that the decoder knows the structure of the source block it is to decode, including the symbol size, T, and the number K of symbols in the source block.
From the algorithms described in Section 5.4, the Raptor decoder can calculate the total number L = K+S+H of pre-coding symbols and determine how they were generated from the source block to be decoded. In this description, it is assumed that the received
From the algorithms described in Section 5.4, the Raptor decoder can calculate the total number L = K+S+H of pre-coding symbols and determine how they were generated from the source block to be decoded. In this description, it is assumed that the received
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Luby, et al. Standards Track [Page 23] RFC 5053 Raptor FEC Scheme October 2007
encoding symbols for the source block to be decoded are passed to the decoder. Note that, as described in Section 5.3.2, the last source symbol of a source packet may have included padding bytes added for FEC encoding purposes. These padding bytes may not be actually included in the packet sent and so must be reinserted at the received before passing the symbol to the decoder.
encoding symbols for the source block to be decoded are passed to the decoder. Note that, as described in Section 5.3.2, the last source symbol of a source packet may have included padding bytes added for FEC encoding purposes. These padding bytes may not be actually included in the packet sent and so must be reinserted at the received before passing the symbol to the decoder.
For each such encoding symbol, it is assumed that the number and set of intermediate symbols whose exclusive-or is equal to the encoding symbol is also passed to the decoder. In the case of source symbols, the source symbol triples described in Section 5.4.2.2 indicate the number and set of intermediate symbols that sum to give each source symbol.
For each such encoding symbol, it is assumed that the number and set of intermediate symbols whose exclusive-or is equal to the encoding symbol is also passed to the decoder. In the case of source symbols, the source symbol triples described in Section 5.4.2.2 indicate the number and set of intermediate symbols that sum to give each source symbol.
Let N >= K be the number of received encoding symbols for a source block and let M = S+H+N. The following M by L bit matrix A can be derived from the information passed to the decoder for the source block to be decoded. Let C be the column vector of the L intermediate symbols, and let D be the column vector of M symbols with values known to the receiver, where the first S+H of the M symbols are zero-valued symbols that correspond to LDPC and Half symbols (these are check symbols for the LDPC and Half symbols, and not the LDPC and Half symbols themselves), and the remaining N of the M symbols are the received encoding symbols for the source block. Then, A is the bit matrix that satisfies A*C = D, where here * denotes matrix multiplication over GF[2]. In particular, A[i,j] = 1 if the intermediate symbol corresponding to index j is exclusive-ORed into the LDPC, Half, or encoding symbol corresponding to index i in the encoding, or if index i corresponds to a LDPC or Half symbol and index j corresponds to the same LDPC or Half symbol. For all other i and j, A[i,j] = 0.
Let N >= K be the number of received encoding symbols for a source block and let M = S+H+N. The following M by L bit matrix A can be derived from the information passed to the decoder for the source block to be decoded. Let C be the column vector of the L intermediate symbols, and let D be the column vector of M symbols with values known to the receiver, where the first S+H of the M symbols are zero-valued symbols that correspond to LDPC and Half symbols (these are check symbols for the LDPC and Half symbols, and not the LDPC and Half symbols themselves), and the remaining N of the M symbols are the received encoding symbols for the source block. Then, A is the bit matrix that satisfies A*C = D, where here * denotes matrix multiplication over GF[2]. In particular, A[i,j] = 1 if the intermediate symbol corresponding to index j is exclusive-ORed into the LDPC, Half, or encoding symbol corresponding to index i in the encoding, or if index i corresponds to a LDPC or Half symbol and index j corresponds to the same LDPC or Half symbol. For all other i and j, A[i,j] = 0.
Decoding a source block is equivalent to decoding C from known A and D. It is clear that C can be decoded if and only if the rank of A over GF[2] is L. Once C has been decoded, missing source symbols can be obtained by using the source symbol triples to determine the number and set of intermediate symbols that MUST be exclusive-ORed to obtain each missing source symbol.
Decoding a source block is equivalent to decoding C from known A and D. It is clear that C can be decoded if and only if the rank of A over GF[2] is L. Once C has been decoded, missing source symbols can be obtained by using the source symbol triples to determine the number and set of intermediate symbols that MUST be exclusive-ORed to obtain each missing source symbol.
The first step in decoding C is to form a decoding schedule. In this
step A is converted, using Gaussian elimination (using row operations
and row and column reorderings) and after discarding M - L rows, into
the L by L identity matrix. The decoding schedule consists of the
sequence of row operations and row and column reorderings during the
Gaussian elimination process, and only depends on A and not on D.
The decoding of C from D can take place concurrently with the
forming of the decoding schedule, or the decoding can take place
afterwards based on the decoding schedule.
The first step in decoding C is to form a decoding schedule. In this step A is converted, using Gaussian elimination (using row operations and row and column reorderings) and after discarding M - L rows, into the L by L identity matrix. The decoding schedule consists of the sequence of row operations and row and column reorderings during the Gaussian elimination process, and only depends on A and not on D. The decoding of C from D can take place concurrently with the forming of the decoding schedule, or the decoding can take place afterwards based on the decoding schedule.
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Luby, et al. Standards Track [Page 24] RFC 5053 Raptor FEC Scheme October 2007
The correspondence between the decoding schedule and the decoding of C is as follows. Let c[0] = 0, c[1] = 1,...,c[L-1] = L-1 and d[0] = 0, d[1] = 1,...,d[M-1] = M-1 initially.
The correspondence between the decoding schedule and the decoding of C is as follows. Let c[0] = 0, c[1] = 1,...,c[L-1] = L-1 and d[0] = 0, d[1] = 1,...,d[M-1] = M-1 initially.
- Each time row i of A is exclusive-ORed into row i' in the decoding
schedule, then in the decoding process, symbol D[d[i]] is
exclusive-ORed into symbol D[d[i']].
- Each time row i of A is exclusive-ORed into row i' in the decoding schedule, then in the decoding process, symbol D[d[i]] is exclusive-ORed into symbol D[d[i']].
- Each time row i is exchanged with row i' in the decoding schedule,
then in the decoding process, the value of d[i] is exchanged with
the value of d[i'].
- Each time row i is exchanged with row i' in the decoding schedule, then in the decoding process, the value of d[i] is exchanged with the value of d[i'].
- Each time column j is exchanged with column j' in the decoding
schedule, then in the decoding process, the value of c[j] is
exchanged with the value of c[j'].
- Each time column j is exchanged with column j' in the decoding schedule, then in the decoding process, the value of c[j] is exchanged with the value of c[j'].
From this correspondence, it is clear that the total number of exclusive-ORs of symbols in the decoding of the source block is the number of row operations (not exchanges) in the Gaussian elimination. Since A is the L by L identity matrix after the Gaussian elimination and after discarding the last M - L rows, it is clear at the end of successful decoding that the L symbols D[d[0]], D[d[1]],..., D[d[L-1]] are the values of the L symbols C[c[0]], C[c[1]],..., C[c[L-1]].
From this correspondence, it is clear that the total number of exclusive-ORs of symbols in the decoding of the source block is the number of row operations (not exchanges) in the Gaussian elimination. Since A is the L by L identity matrix after the Gaussian elimination and after discarding the last M - L rows, it is clear at the end of successful decoding that the L symbols D[d[0]], D[d[1]],..., D[d[L-1]] are the values of the L symbols C[c[0]], C[c[1]],..., C[c[L-1]].
The order in which Gaussian elimination is performed to form the decoding schedule has no bearing on whether or not the decoding is successful. However, the speed of the decoding depends heavily on the order in which Gaussian elimination is performed. (Furthermore, maintaining a sparse representation of A is crucial, although this is not described here). The remainder of this section describes an order in which Gaussian elimination could be performed that is relatively efficient.
The order in which Gaussian elimination is performed to form the decoding schedule has no bearing on whether or not the decoding is successful. However, the speed of the decoding depends heavily on the order in which Gaussian elimination is performed. (Furthermore, maintaining a sparse representation of A is crucial, although this is not described here). The remainder of this section describes an order in which Gaussian elimination could be performed that is relatively efficient.
5.5.2.2. First Phase
5.5.2.2. First Phase
The first phase of the Gaussian elimination, the matrix A, is conceptually partitioned into submatrices. The submatrix sizes are parameterized by non-negative integers i and u, which are initialized to 0. The submatrices of A are:
The first phase of the Gaussian elimination, the matrix A, is conceptually partitioned into submatrices. The submatrix sizes are parameterized by non-negative integers i and u, which are initialized to 0. The submatrices of A are:
(1) The submatrix I defined by the intersection of the first i
rows and first i columns. This is the identity matrix at the
end of each step in the phase.
(1) The submatrix I defined by the intersection of the first i rows and first i columns. This is the identity matrix at the end of each step in the phase.
(2) The submatrix defined by the intersection of the first i rows
and all but the first i columns and last u columns. All
entries of this submatrix are zero.
(2) The submatrix defined by the intersection of the first i rows and all but the first i columns and last u columns. All entries of this submatrix are zero.
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Luby, et al. Standards Track [Page 25] RFC 5053 Raptor FEC Scheme October 2007
(3) The submatrix defined by the intersection of the first i
columns and all but the first i rows. All entries of this
submatrix are zero.
(3) 最初iのコラムとすべての交差点によって定義された部分行列にもかかわらず、最初のiは船をこぎます。 この部分行列のすべてのエントリーがゼロです。
(4) The submatrix U defined by the intersection of all the rows
and the last u columns.
(4) すべての列と最後のuコラムの交差点によって定義された部分行列U。
(5) The submatrix V formed by the intersection of all but the
first i columns and the last u columns and all but the first i
rows.
(5) 部分行列Vは1番目を除いたすべての交差点のそばでiコラム、最後のuコラム、および1番目を除いた私がこぐすべてを形成しました。
Figure 5 illustrates the submatrices of A. At the beginning of the first phase, V = A. In each step, a row of A is chosen.
図5はA.第1段階、Vの始まり=Inがそれぞれ踏むA.Atの「副-マトリクス」を例証して、Aの列は選ばれています。
+-----------+-----------------+---------+ | | | | | I | All Zeros | | | | | | +-----------+-----------------+ U | | | | | | | | | | All Zeros | V | | | | | | | | | | +-----------+-----------------+---------+
+-----------+-----------------+---------+ | | | | | I| すべてのゼロ| | | | | | +-----------+-----------------+ U| | | | | | | | | | すべてのゼロ| V| | | | | | | | | | +-----------+-----------------+---------+
Figure 5: Submatrices of A in the first phase
図5: 第1段階におけるAのSubmatrices
The following graph defined by the structure of V is used in determining which row of A is chosen. The columns that intersect V are the nodes in the graph, and the rows that have exactly 2 ones in V are the edges of the graph that connect the two columns (nodes) in the positions of the two ones. A component in this graph is a maximal set of nodes (columns) and edges (rows) such that there is a path between each pair of nodes/edges in the graph. The size of a component is the number of nodes (columns) in the component.
どの列のAが選ばれているかを決定する際にVの構造によって定義された以下のグラフは使用されます。 それは交差しています。コラム、グラフでVはノードであり、まさにVの2つのものを持っている列は2つのものの位置の2つのコラム(ノード)を接続するグラフの縁です。 このグラフによるコンポーネントは、それぞれの組のノード/縁の間には、グラフに経路があるための最大限度のセットのノード(コラム)と縁(列)です。 コンポーネントのサイズはコンポーネントのノード(コラム)の数です。
There are at most L steps in the first phase. The phase ends successfully when i + u = L, i.e., when V and the all-zeroes submatrix above V have disappeared and A consists of I, the all zeroes submatrix below I, and U. The phase ends unsuccessfully in decoding failure if, at some step before V disappears, there is no non-zero row in V to choose in that step. Whenever there are non- zero rows in V, then the next step starts by choosing a row of A as follows:
Lステップが第1段階に高々あります。 i+uがLと等しいと、フェーズは首尾よく終わります、すなわち、VとVの上のオールゼロ部分行列が見えなくなって、AがIから成るとすべてが部分行列のゼロに合っている、以下に、私、およびそれで選ぶために非ゼロ列が全くVにVが見えなくなる前の何らかのステップになければ失敗を解読するフェーズが終わって失敗したU.が踏まれます。 あるときはいつも、非ゼロはVで船をこぎます、次に、次のステップは以下のAの列を選ぶことによって、始まります:
Luby, et al. Standards Track [Page 26] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[26ページ]。
o Let r be the minimum integer such that at least one row of A has
exactly r ones in V.
o 少なくとも1つの列のAにはまさにVのrものがあるように、rが最小の整数であることをさせてください。
* If r != 2, then choose a row with exactly r ones in V with
minimum original degree among all such rows.
* r!=2であるなら、まさにrものがVにある状態で、そのようなすべての列の中で最小の元の度で列を選んでください。
* If r = 2, then choose any row with exactly 2 ones in V that is
part of a maximum size component in the graph defined by V.
* r=2であるなら、まさに2つのものが最大サイズ成分の一部であるVにある状態で、Vによって定義されたグラフであらゆる列を選んでください。
After the row is chosen in this step the first row of A that intersects V is exchanged with the chosen row so that the chosen row is the first row that intersects V. The columns of A among those that intersect V are reordered so that one of the r ones in the chosen row appears in the first column of V and so that the remaining r-1 ones appear in the last columns of V. Then, the chosen row is exclusive-ORed into all the other rows of A below the chosen row that have a one in the first column of V. Finally, i is incremented by 1 and u is incremented by r-1, which completes the step.
列がことになったこのステップの交差するAのファースト・ローが選ばれて、Vが交換して、選ぶことで、V. 交差するもののAに関するコラムが選ばれた列が横切られるファースト・ローであるように船をこいでいるということであるという後にVが再命令されるので、選ばれた列のrものの1つは最初のコラムのVに現れて、残っているr-1人はVに関する最後のコラムに現れます; 次に、選ばれた列は選ばれた列の下の他のすべての列のAへのV.Finallyの最初のコラムの1つを持っている排他的なORedです、そして、iは1つ増加されます、そして、uはr-1によって増加されます。(r-1はステップを終了します)。
5.5.2.3. Second Phase
5.5.2.3. 第2フェーズ
The submatrix U is further partitioned into the first i rows, U_upper, and the remaining M - i rows, U_lower. Gaussian elimination is performed in the second phase on U_lower to either determine that its rank is less than u (decoding failure) or to convert it into a matrix where the first u rows is the identity matrix (success of the second phase). Call this u by u identity matrix I_u. The M - L rows of A that intersect U_lower - I_u are discarded. After this phase, A has L rows and L columns.
部分行列Uはさらに1番目にi列で、U_上側で仕切られます、そして、残っているM--i列、U_は下ろします。 ガウス消去法は2番目のフェーズでランクがu以下(失敗を解読して)であるか最初のuが船をこぐマトリクスにそれを変換するのが、アイデンティティマトリクス(2番目のフェーズの成功)であることを決定するためには下側のU_に実行されます。 uアイデンティティマトリクスI_uでこのuを呼んでください。 M--Lは交差するAをこぎます。U_は下ろします--I_uは捨てられます。 このフェーズの後に、Aには、L列とLコラムがあります。
5.5.2.4. Third Phase
5.5.2.4. 第3フェーズ
After the second phase, the only portion of A that needs to be zeroed out to finish converting A into the L by L identity matrix is U_upper. The number of rows i of the submatrix U_upper is generally much larger than the number of columns u of U_upper. To zero out U_upper efficiently, the following precomputation matrix U' is computed based on I_u in the third phase and then U' is used in the fourth phase to zero out U_upper. The u rows of Iu are partitioned into ceil(u/8) groups of 8 rows each. Then, for each group of 8 rows, all non-zero combinations of the 8 rows are computed, resulting in 2^^8 - 1 = 255 rows (this can be done with 2^^8-8-1 = 247 exclusive-ors of rows per group, since the combinations of Hamming weight one that appear in I_u do not need to be recomputed). Thus, the resulting precomputation matrix U' has ceil(u/8)*255 rows and u columns. Note that U' is not formally a part of matrix A, but will be used in the fourth phase to zero out U_upper.
2番目のフェーズの後に、外にLアイデンティティマトリクスでAをLに変換し終えるためにゼロに合わせられる必要があるAの唯一の部がU_上です。 一般に、_部分行列Uの列iより上にの数はU_覚醒剤に関するコラムuの数よりはるかに大きいです。 '_より上に効率的に出かけているUのゼロを合わせるために、以下の前計算マトリクスU'は3番目のフェーズにおけるI_uと次に、Uに基づいて計算されること'は_より上に出かけているUのゼロを合わせる4番目のフェーズに使用されます。 Iuのu列はそれぞれ8つの列のceil(u/8)グループに仕切られます。 次に、8つの列の各グループにおいて、8つの列のすべての非ゼロ組み合わせが計算されます、2^^8をもたらして--1 = 255 列(1グループあたりの列の2^^8-8-1 = 247の排他的なorsでこれができます、I_uに現れるハミング重さ1の組み合わせが再計算される必要はないので)。 'その結果、結果として起こる前計算マトリクスU'には、ceil(u/8)*255列とuコラムがあります。 'U'が正式に、aがマトリクスAを離れさせるということではありませんが、_より上に出かけているUのゼロを合わせる4番目のフェーズに使用されることに注意してください。
Luby, et al. Standards Track [Page 27] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[27ページ]。
5.5.2.5. Fourth Phase
5.5.2.5. 第4フェーズ
For each of the first i rows of A, for each group of 8 columns in the U_upper submatrix of this row, if the set of 8 column entries in U_upper are not all zero, then the row of the precomputation matrix U' that matches the pattern in the 8 columns is exclusive-ORed into the row, thus zeroing out those 8 columns in the row at the cost of exclusive-ORing one row of U' into the row.
'それぞれの1番目に関して、私はAをこぎます、この列のU_の上側の部分行列における8つのコラムの各グループのためにU_の8つのコラムエントリーのセットであるなら上側であることが、すべてゼロであるというわけではなく、次に、8つのコラムのパターンに合っている前計算マトリクスU'の列は列への唯一のORedです、その結果、外で排他的なORing1つの列のU'の費用で列のそれらの8つのコラムのゼロを列に合わせます。
After this phase, A is the L by L identity matrix and a complete decoding schedule has been successfully formed. Then, as explained in Section 5.5.2.1, the corresponding decoding consisting of exclusive-ORing known encoding symbols can be executed to recover the intermediate symbols based on the decoding schedule. The triples associated with all source symbols are computed according to Section 5.4.2.2. The triples for received source symbols are used in the decoding. The triples for missing source symbols are used to determine which intermediate symbols need to be exclusive-ORed to recover the missing source symbols.
このフェーズの後に、LアイデンティティマトリクスによってAはLです、そして、首尾よく完全な解読スケジュールを形成してあります。 そして、セクション5.5.2で.1について説明するとき、解読スケジュールに基づく中間的シンボルを回復するためにシンボルをコード化しながら知られている排他的なORingから成る対応する解読は実行できます。 セクション5.4.2に従って、すべてのソースシンボルに関連している三重は.2に計算されます。 容認されたソースシンボルのための三重は解読に使用されます。 なくなったソースシンボルのための三重は、どの中間的シンボルが、なくなったソースシンボルを回復するのに排他的なORedである必要であるかを決定するのに使用されます。
5.6. Random Numbers
5.6. 乱数
The two tables V0 and V1 described in Section 5.4.4.1 are given below. Each entry is a 32-bit integer in decimal representation.
V0とV1が.1が与えられているセクション5.4.4で説明した2個のテーブル。 各エントリーは10進表現で32ビットの整数です。
5.6.1. The Table V0
5.6.1. テーブルV0
251291136, 3952231631, 3370958628, 4070167936, 123631495, 3351110283, 3218676425, 2011642291, 774603218, 2402805061, 1004366930, 1843948209, 428891132, 3746331984, 1591258008, 3067016507, 1433388735, 504005498, 2032657933, 3419319784, 2805686246, 3102436986, 3808671154, 2501582075, 3978944421, 246043949, 4016898363, 649743608, 1974987508, 2651273766, 2357956801, 689605112, 715807172, 2722736134, 191939188, 3535520147, 3277019569, 1470435941, 3763101702, 3232409631, 122701163, 3920852693, 782246947, 372121310, 2995604341, 2045698575, 2332962102, 4005368743, 218596347, 3415381967, 4207612806, 861117671, 3676575285, 2581671944, 3312220480, 681232419, 307306866, 4112503940, 1158111502, 709227802, 2724140433, 4201101115, 4215970289, 4048876515, 3031661061, 1909085522, 510985033, 1361682810, 129243379, 3142379587, 2569842483, 3033268270, 1658118006, 932109358, 1982290045, 2983082771, 3007670818, 3448104768, 683749698, 778296777, 1399125101, 1939403708, 1692176003, 3868299200, 1422476658, 593093658, 1878973865, 2526292949, 1591602827, 3986158854, 3964389521, 2695031039, 1942050155, 424618399, 1347204291, 2669179716, 2434425874, 2540801947, 1384069776, 4123580443, 1523670218, 2708475297, 1046771089, 2229796016, 1255426612, 4213663089, 1521339547, 3041843489, 420130494, 10677091, 515623176, 3457502702, 2115821274,
251291136, 3952231631, 3370958628, 4070167936, 123631495, 3351110283, 3218676425, 2011642291, 774603218, 2402805061, 1004366930, 1843948209, 428891132, 3746331984, 1591258008, 3067016507, 1433388735, 504005498, 2032657933, 3419319784, 2805686246, 3102436986, 3808671154, 2501582075, 3978944421, 246043949, 4016898363, 649743608, 1974987508, 2651273766, 2357956801, 689605112, 715807172, 2722736134, 191939188, 3535520147, 3277019569, 1470435941, 3763101702, 3232409631, 122701163, 3920852693, 782246947, 372121310, 2995604341, 2045698575, 2332962102, 4005368743, 218596347, 3415381967, 4207612806, 861117671, 3676575285, 2581671944, 3312220480, 681232419, 307306866, 4112503940, 1158111502, 709227802, 2724140433, 4201101115, 4215970289, 4048876515, 3031661061, 1909085522, 510985033, 1361682810, 129243379, 3142379587, 2569842483, 3033268270, 1658118006, 932109358, 1982290045, 2983082771, 3007670818, 3448104768, 683749698, 778296777, 1399125101, 1939403708, 1692176003, 3868299200, 1422476658, 593093658, 1878973865, 2526292949, 1591602827, 3986158854, 3964389521, 2695031039, 1942050155, 424618399, 1347204291, 2669179716, 2434425874, 2540801947, 1384069776, 4123580443, 1523670218, 2708475297, 1046771089, 2229796016, 1255426612, 4213663089, 1521339547, 3041843489, 420130494, 10677091, 515623176, 3457502702, 2115821274,
Luby, et al. Standards Track [Page 28] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[28ページ]。
2720124766, 3242576090, 854310108, 425973987, 325832382, 1796851292, 2462744411, 1976681690, 1408671665, 1228817808, 3917210003, 263976645, 2593736473, 2471651269, 4291353919, 650792940, 1191583883, 3046561335, 2466530435, 2545983082, 969168436, 2019348792, 2268075521, 1169345068, 3250240009, 3963499681, 2560755113, 911182396, 760842409, 3569308693, 2687243553, 381854665, 2613828404, 2761078866, 1456668111, 883760091, 3294951678, 1604598575, 1985308198, 1014570543, 2724959607, 3062518035, 3115293053, 138853680, 4160398285, 3322241130, 2068983570, 2247491078, 3669524410, 1575146607, 828029864, 3732001371, 3422026452, 3370954177, 4006626915, 543812220, 1243116171, 3928372514, 2791443445, 4081325272, 2280435605, 885616073, 616452097, 3188863436, 2780382310, 2340014831, 1208439576, 258356309, 3837963200, 2075009450, 3214181212, 3303882142, 880813252, 1355575717, 207231484, 2420803184, 358923368, 1617557768, 3272161958, 1771154147, 2842106362, 1751209208, 1421030790, 658316681, 194065839, 3241510581, 38625260, 301875395, 4176141739, 297312930, 2137802113, 1502984205, 3669376622, 3728477036, 234652930, 2213589897, 2734638932, 1129721478, 3187422815, 2859178611, 3284308411, 3819792700, 3557526733, 451874476, 1740576081, 3592838701, 1709429513, 3702918379, 3533351328, 1641660745, 179350258, 2380520112, 3936163904, 3685256204, 3156252216, 1854258901, 2861641019, 3176611298, 834787554, 331353807, 517858103, 3010168884, 4012642001, 2217188075, 3756943137, 3077882590, 2054995199, 3081443129, 3895398812, 1141097543, 2376261053, 2626898255, 2554703076, 401233789, 1460049922, 678083952, 1064990737, 940909784, 1673396780, 528881783, 1712547446, 3629685652, 1358307511
2720124766, 3242576090, 854310108, 425973987, 325832382, 1796851292, 2462744411, 1976681690, 1408671665, 1228817808, 3917210003, 263976645, 2593736473, 2471651269, 4291353919, 650792940, 1191583883, 3046561335, 2466530435, 2545983082, 969168436, 2019348792, 2268075521, 1169345068, 3250240009, 3963499681, 2560755113, 911182396, 760842409, 3569308693, 2687243553, 381854665, 2613828404, 2761078866, 1456668111, 883760091, 3294951678, 1604598575, 1985308198, 1014570543, 2724959607, 3062518035, 3115293053, 138853680, 4160398285, 3322241130, 2068983570, 2247491078, 3669524410, 1575146607, 828029864, 3732001371, 3422026452, 3370954177, 4006626915, 543812220, 1243116171, 3928372514, 2791443445, 4081325272, 2280435605, 885616073, 616452097, 3188863436, 2780382310, 2340014831, 1208439576, 258356309, 3837963200, 2075009450, 3214181212, 3303882142, 880813252, 1355575717, 207231484, 2420803184, 358923368, 1617557768, 3272161958, 1771154147, 2842106362, 1751209208, 1421030790, 658316681, 194065839, 3241510581, 38625260, 301875395, 4176141739, 297312930, 2137802113, 1502984205, 3669376622, 3728477036, 234652930, 2213589897, 2734638932, 1129721478, 3187422815, 2859178611, 3284308411, 3819792700, 3557526733, 451874476, 1740576081, 3592838701, 1709429513, 3702918379, 3533351328, 1641660745, 179350258, 2380520112, 3936163904, 3685256204, 3156252216, 1854258901, 2861641019, 3176611298, 834787554, 331353807, 517858103, 3010168884, 4012642001, 2217188075, 3756943137, 3077882590, 2054995199, 3081443129, 3895398812, 1141097543, 2376261053, 2626898255, 2554703076, 401233789, 1460049922, 678083952, 1064990737, 940909784, 1673396780, 528881783, 1712547446, 3629685652, 1358307511
5.6.2. The Table V1
5.6.2. テーブルV1
807385413, 2043073223, 3336749796, 1302105833, 2278607931, 541015020, 1684564270, 372709334, 3508252125, 1768346005, 1270451292, 2603029534, 2049387273, 3891424859, 2152948345, 4114760273, 915180310, 3754787998, 700503826, 2131559305, 1308908630, 224437350, 4065424007, 3638665944, 1679385496, 3431345226, 1779595665, 3068494238, 1424062773, 1033448464, 4050396853, 3302235057, 420600373, 2868446243, 311689386, 259047959, 4057180909, 1575367248, 4151214153, 110249784, 3006865921, 4293710613, 3501256572, 998007483, 499288295, 1205710710, 2997199489, 640417429, 3044194711, 486690751, 2686640734, 2394526209, 2521660077, 49993987, 3843885867, 4201106668, 415906198, 19296841, 2402488407, 2137119134, 1744097284, 579965637, 2037662632, 852173610, 2681403713, 1047144830, 2982173936, 910285038, 4187576520, 2589870048, 989448887, 3292758024, 506322719, 176010738, 1865471968, 2619324712, 564829442, 1996870325, 339697593, 4071072948, 3618966336, 2111320126, 1093955153, 957978696, 892010560, 1854601078, 1873407527, 2498544695, 2694156259, 1927339682, 1650555729, 183933047, 3061444337, 2067387204, 228962564, 3904109414, 1595995433, 1780701372, 2463145963, 307281463, 3237929991, 3852995239,
807385413, 2043073223, 3336749796, 1302105833, 2278607931, 541015020, 1684564270, 372709334, 3508252125, 1768346005, 1270451292, 2603029534, 2049387273, 3891424859, 2152948345, 4114760273, 915180310, 3754787998, 700503826, 2131559305, 1308908630, 224437350, 4065424007, 3638665944, 1679385496, 3431345226, 1779595665, 3068494238, 1424062773, 1033448464, 4050396853, 3302235057, 420600373, 2868446243, 311689386, 259047959, 4057180909, 1575367248, 4151214153, 110249784, 3006865921, 4293710613, 3501256572, 998007483, 499288295, 1205710710, 2997199489, 640417429, 3044194711, 486690751, 2686640734, 2394526209, 2521660077, 49993987, 3843885867, 4201106668, 415906198, 19296841, 2402488407, 2137119134, 1744097284, 579965637, 2037662632, 852173610, 2681403713, 1047144830, 2982173936, 910285038, 4187576520, 2589870048, 989448887, 3292758024, 506322719, 176010738, 1865471968, 2619324712, 564829442, 1996870325, 339697593, 4071072948, 3618966336, 2111320126, 1093955153, 957978696, 892010560, 1854601078, 1873407527, 2498544695, 2694156259, 1927339682, 1650555729, 183933047, 3061444337, 2067387204, 228962564, 3904109414, 1595995433, 1780701372, 2463145963, 307281463, 3237929991, 3852995239,
Luby, et al. Standards Track [Page 29] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[29ページ]。
2398693510, 3754138664, 522074127, 146352474, 4104915256, 3029415884, 3545667983, 332038910, 976628269, 3123492423, 3041418372, 2258059298, 2139377204, 3243642973, 3226247917, 3674004636, 2698992189, 3453843574, 1963216666, 3509855005, 2358481858, 747331248, 1957348676, 1097574450, 2435697214, 3870972145, 1888833893, 2914085525, 4161315584, 1273113343, 3269644828, 3681293816, 412536684, 1156034077, 3823026442, 1066971017, 3598330293, 1979273937, 2079029895, 1195045909, 1071986421, 2712821515, 3377754595, 2184151095, 750918864, 2585729879, 4249895712, 1832579367, 1192240192, 946734366, 31230688, 3174399083, 3549375728, 1642430184, 1904857554, 861877404, 3277825584, 4267074718, 3122860549, 666423581, 644189126, 226475395, 307789415, 1196105631, 3191691839, 782852669, 1608507813, 1847685900, 4069766876, 3931548641, 2526471011, 766865139, 2115084288, 4259411376, 3323683436, 568512177, 3736601419, 1800276898, 4012458395, 1823982, 27980198, 2023839966, 869505096, 431161506, 1024804023, 1853869307, 3393537983, 1500703614, 3019471560, 1351086955, 3096933631, 3034634988, 2544598006, 1230942551, 3362230798, 159984793, 491590373, 3993872886, 3681855622, 903593547, 3535062472, 1799803217, 772984149, 895863112, 1899036275, 4187322100, 101856048, 234650315, 3183125617, 3190039692, 525584357, 1286834489, 455810374, 1869181575, 922673938, 3877430102, 3422391938, 1414347295, 1971054608, 3061798054, 830555096, 2822905141, 167033190, 1079139428, 4210126723, 3593797804, 429192890, 372093950, 1779187770, 3312189287, 204349348, 452421568, 2800540462, 3733109044, 1235082423, 1765319556, 3174729780, 3762994475, 3171962488, 442160826, 198349622, 45942637, 1324086311, 2901868599, 678860040, 3812229107, 19936821, 1119590141, 3640121682, 3545931032, 2102949142, 2828208598, 3603378023, 4135048896
2398693510, 3754138664, 522074127, 146352474, 4104915256, 3029415884, 3545667983, 332038910, 976628269, 3123492423, 3041418372, 2258059298, 2139377204, 3243642973, 3226247917, 3674004636, 2698992189, 3453843574, 1963216666, 3509855005, 2358481858, 747331248, 1957348676, 1097574450, 2435697214, 3870972145, 1888833893, 2914085525, 4161315584, 1273113343, 3269644828, 3681293816, 412536684, 1156034077, 3823026442, 1066971017, 3598330293, 1979273937, 2079029895, 1195045909, 1071986421, 2712821515, 3377754595, 2184151095, 750918864, 2585729879, 4249895712, 1832579367, 1192240192, 946734366, 31230688, 3174399083, 3549375728, 1642430184, 1904857554, 861877404, 3277825584, 4267074718, 3122860549, 666423581, 644189126, 226475395, 307789415, 1196105631, 3191691839, 782852669, 1608507813, 1847685900, 4069766876, 3931548641, 2526471011, 766865139, 2115084288, 4259411376, 3323683436, 568512177, 3736601419, 1800276898, 4012458395, 1823982, 27980198, 2023839966, 869505096, 431161506, 1024804023, 1853869307, 3393537983, 1500703614, 3019471560, 1351086955, 3096933631, 3034634988, 2544598006, 1230942551, 3362230798, 159984793, 491590373, 3993872886, 3681855622, 903593547, 3535062472, 1799803217, 772984149, 895863112, 1899036275, 4187322100, 101856048, 234650315, 3183125617, 3190039692, 525584357, 1286834489, 455810374, 1869181575, 922673938, 3877430102, 3422391938, 1414347295, 1971054608, 3061798054, 830555096, 2822905141, 167033190, 1079139428, 4210126723, 3593797804, 429192890, 372093950, 1779187770, 3312189287, 204349348, 452421568, 2800540462, 3733109044, 1235082423, 1765319556, 3174729780, 3762994475, 3171962488, 442160826, 198349622, 45942637, 1324086311, 2901868599, 678860040, 3812229107, 19936821, 1119590141, 3640121682, 3545931032, 2102949142, 2828208598, 3603378023, 4135048896
5.7. Systematic Indices J(K)
5.7. 系統的なインデックスリストJ(K)
For each value of K, the systematic index J(K) is designed to have the property that the set of source symbol triples (d[0], a[0], b[0]), ..., (d[L-1], a[L-1], b[L-1]) are such that the L intermediate symbols are uniquely defined, i.e., the matrix A in Section 5.4.2.4.2 has full rank and is therefore invertible.
Kの各値において、系統的なインデックスJ(K)がソースシンボルのセットが3倍にする特性を持つように設計されている、(d[0]、a[0]、b[0])…, (d[L-1]、[L-1]、b[L-1]) L中間的シンボルが唯一定義されて、すなわち、セクション5.4.2におけるマトリクスAが.2が持っている.4であるようにものは完全なランクです、そして、したがって、invertibleはそのようなランクですか?
The following is the list of the systematic indices for values of K between 4 and 8192 inclusive.
↓これは4と8192の間で包括的なKの値のための系統的なインデックスリストのリストです。
18, 14, 61, 46, 14, 22, 20, 40, 48, 1, 29, 40, 43, 46, 18, 8, 20, 2, 61, 26, 13, 29, 36, 19, 58, 5, 58, 0, 54, 56, 24, 14, 5, 67, 39, 31, 25, 29, 24, 19, 14, 56, 49, 49, 63, 30, 4, 39, 2, 1, 20, 19, 61, 4, 54, 70, 25, 52, 9, 26, 55, 69, 27, 68, 75, 19, 64, 57, 45, 3, 37, 31, 100, 41, 25, 41, 53, 23, 9, 31, 26, 30, 30, 46, 90, 50, 13, 90, 77, 61, 31, 54, 54, 3, 21, 66, 21, 11, 23, 11, 29, 21, 7, 1, 27, 4, 34, 17, 85, 69, 17, 75, 93, 57, 0, 53, 71, 88, 119, 88, 90, 22, 0, 58, 41, 22, 96, 26, 79, 118, 19, 3, 81, 72, 50, 0, 32, 79, 28, 25, 12,
18, 14, 61, 46, 14, 22, 20, 40, 48, 1, 29, 40, 43, 46, 18, 8, 20, 2, 61, 26, 13, 29, 36, 19, 58, 5, 58, 0, 54, 56, 24, 14, 5, 67, 39, 31, 25, 29, 24, 19, 14, 56, 49, 49, 63, 30, 4, 39, 2, 1, 20, 19, 61, 4, 54, 70, 25, 52, 9, 26, 55, 69, 27, 68, 75, 19, 64, 57, 45, 3, 37, 31, 100, 41, 25, 41, 53, 23, 9, 31, 26, 30, 30, 46, 90, 50, 13, 90, 77, 61, 31, 54, 54, 3, 21, 66, 21, 11, 23, 11, 29, 21, 7, 1, 27, 4, 34, 17, 85, 69, 17, 75, 93, 57, 0, 53, 71, 88, 119, 88, 90, 22, 0, 58, 41, 22, 96, 26, 79, 118, 19, 3, 81, 72, 50, 0, 32, 79, 28, 25, 12,
Luby, et al. Standards Track [Page 30] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[30ページ]。
25, 29, 3, 37, 30, 30, 41, 84, 32, 31, 61, 32, 61, 7, 56, 54, 39, 33, 66, 29, 3, 14, 75, 75, 78, 84, 75, 84, 25, 54, 25, 25, 107, 78, 27, 73, 0, 49, 96, 53, 50, 21, 10, 73, 58, 65, 27, 3, 27, 18, 54, 45, 69, 29, 3, 65, 31, 71, 76, 56, 54, 76, 54, 13, 5, 18, 142, 17, 3, 37, 114, 41, 25, 56, 0, 23, 3, 41, 22, 22, 31, 18, 48, 31, 58, 37, 75, 88, 3, 56, 1, 95, 19, 73, 52, 52, 4, 75, 26, 1, 25, 10, 1, 70, 31, 31, 12, 10, 54, 46, 11, 74, 84, 74, 8, 58, 23, 74, 8, 36, 11, 16, 94, 76, 14, 57, 65, 8, 22, 10, 36, 36, 96, 62, 103, 6, 75, 103, 58, 10, 15, 41, 75, 125, 58, 15, 10, 34, 29, 34, 4, 16, 29, 18, 18, 28, 71, 28, 43, 77, 18, 41, 41, 41, 62, 29, 96, 15, 106, 43, 15, 3, 43, 61, 3, 18, 103, 77, 29, 103, 19, 58, 84, 58, 1, 146, 32, 3, 70, 52, 54, 29, 70, 69, 124, 62, 1, 26, 38, 26, 3, 16, 26, 5, 51, 120, 41, 16, 1, 43, 34, 34, 29, 37, 56, 29, 96, 86, 54, 25, 84, 50, 34, 34, 93, 84, 96, 29, 29, 50, 50, 6, 1, 105, 78, 15, 37, 19, 50, 71, 36, 6, 54, 8, 28, 54, 75, 75, 16, 75, 131, 5, 25, 16, 69, 17, 69, 6, 96, 53, 96, 41, 119, 6, 6, 88, 50, 88, 52, 37, 0, 124, 73, 73, 7, 14, 36, 69, 79, 6, 114, 40, 79, 17, 77, 24, 44, 37, 69, 27, 37, 29, 33, 37, 50, 31, 69, 29, 101, 7, 61, 45, 17, 73, 37, 34, 18, 94, 22, 22, 63, 3, 25, 25, 17, 3, 90, 34, 34, 41, 34, 41, 54, 41, 54, 41, 41, 41, 163, 143, 96, 18, 32, 39, 86, 104, 11, 17, 17, 11, 86, 104, 78, 70, 52, 78, 17, 73, 91, 62, 7, 128, 50, 124, 18, 101, 46, 10, 75, 104, 73, 58, 132, 34, 13, 4, 95, 88, 33, 76, 74, 54, 62, 113, 114, 103, 32, 103, 69, 54, 53, 3, 11, 72, 31, 53, 102, 37, 53, 11, 81, 41, 10, 164, 10, 41, 31, 36, 113, 82, 3, 125, 62, 16, 4, 41, 41, 4, 128, 49, 138, 128, 74, 103, 0, 6, 101, 41, 142, 171, 39, 105, 121, 81, 62, 41, 81, 37, 3, 81, 69, 62, 3, 69, 70, 21, 29, 4, 91, 87, 37, 79, 36, 21, 71, 37, 41, 75, 128, 128, 15, 25, 3, 108, 73, 91, 62, 114, 62, 62, 36, 36, 15, 58, 114, 61, 114, 58, 105, 114, 41, 61, 176, 145, 46, 37, 30, 220, 77, 138, 15, 1, 128, 53, 50, 50, 58, 8, 91, 114, 105, 63, 91, 37, 37, 13, 169, 51, 102, 6, 102, 23, 105, 23, 58, 6, 29, 29, 19, 82, 29, 13, 36, 27, 29, 61, 12, 18, 127, 127, 12, 44, 102, 18, 4, 15, 206, 53, 127, 53, 17, 69, 69, 69, 29, 29, 109, 25, 102, 25, 53, 62, 99, 62, 62, 29, 62, 62, 45, 91, 125, 29, 29, 29, 4, 117, 72, 4, 30, 71, 71, 95, 79, 179, 71, 30, 53, 32, 32, 49, 25, 91, 25, 26, 26, 103, 123, 26, 41, 162, 78, 52, 103, 25, 6, 142, 94, 45, 45, 94, 127, 94, 94, 94, 47, 209, 138, 39, 39, 19, 154, 73, 67, 91, 27, 91, 84, 4, 84, 91, 12, 14, 165, 142, 54, 69, 192, 157, 185, 8, 95, 25, 62, 103, 103, 95, 71, 97, 62, 128, 0, 29, 51, 16, 94, 16, 16, 51, 0, 29, 85, 10, 105, 16, 29, 29, 13, 29, 4, 4, 132, 23, 95, 25, 54, 41, 29, 50, 70, 58, 142, 72, 70, 15, 72, 54, 29, 22, 145, 29, 127, 29, 85, 58, 101, 34, 165, 91, 46, 46, 25, 185, 25, 77, 128, 46, 128, 46, 188, 114, 46, 25, 45, 45, 114, 145, 114, 15, 102, 142, 8, 73, 31, 139, 157, 13, 79, 13, 114, 150, 8, 90, 91, 123, 69, 82, 132, 8, 18, 10, 102, 103, 114, 103, 8, 103, 13, 115, 55, 62, 3, 8, 154, 114, 99, 19, 8, 31, 73, 19, 99, 10, 6, 121, 32, 13, 32, 119, 32, 29, 145, 30, 13, 13, 114, 145, 32, 1, 123, 39, 29, 31, 69, 31, 140, 72, 72, 25, 25, 123, 25, 123, 8, 4, 85, 8, 25, 39, 25, 39, 85, 138, 25, 138, 25, 33, 102, 70, 25, 25, 31, 25, 25, 192, 69, 69, 114, 145, 120, 120, 8, 33, 98, 15, 212, 155, 8,
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Luby, et al. Standards Track [Page 31] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[31ページ]。
101, 8, 8, 98, 68, 155, 102, 132, 120, 30, 25, 123, 123, 101, 25, 123, 32, 24, 94, 145, 32, 24, 94, 118, 145, 101, 53, 53, 25, 128, 173, 142, 81, 81, 69, 33, 33, 125, 4, 1, 17, 27, 4, 17, 102, 27, 13, 25, 128, 71, 13, 39, 53, 13, 53, 47, 39, 23, 128, 53, 39, 47, 39, 135, 158, 136, 36, 36, 27, 157, 47, 76, 213, 47, 156, 25, 25, 53, 25, 53, 25, 86, 27, 159, 25, 62, 79, 39, 79, 25, 145, 49, 25, 143, 13, 114, 150, 130, 94, 102, 39, 4, 39, 61, 77, 228, 22, 25, 47, 119, 205, 122, 119, 205, 119, 22, 119, 258, 143, 22, 81, 179, 22, 22, 143, 25, 65, 53, 168, 36, 79, 175, 37, 79, 70, 79, 103, 70, 25, 175, 4, 96, 96, 49, 128, 138, 96, 22, 62, 47, 95, 105, 95, 62, 95, 62, 142, 103, 69, 103, 30, 103, 34, 173, 127, 70, 127, 132, 18, 85, 22, 71, 18, 206, 206, 18, 128, 145, 70, 193, 188, 8, 125, 114, 70, 128, 114, 145, 102, 25, 12, 108, 102, 94, 10, 102, 1, 102, 124, 22, 22, 118, 132, 22, 116, 75, 41, 63, 41, 189, 208, 55, 85, 69, 8, 71, 53, 71, 69, 102, 165, 41, 99, 69, 33, 33, 29, 156, 102, 13, 251, 102, 25, 13, 109, 102, 164, 102, 164, 102, 25, 29, 228, 29, 259, 179, 222, 95, 94, 30, 30, 30, 142, 55, 142, 72, 55, 102, 128, 17, 69, 164, 165, 3, 164, 36, 165, 27, 27, 45, 21, 21, 237, 113, 83, 231, 106, 13, 154, 13, 154, 128, 154, 148, 258, 25, 154, 128, 3, 27, 10, 145, 145, 21, 146, 25, 1, 185, 121, 0, 1, 95, 55, 95, 95, 30, 0, 27, 95, 0, 95, 8, 222, 27, 121, 30, 95, 121, 0, 98, 94, 131, 55, 95, 95, 30, 98, 30, 0, 91, 145, 66, 179, 66, 58, 175, 29, 0, 31, 173, 146, 160, 39, 53, 28, 123, 199, 123, 175, 146, 156, 54, 54, 149, 25, 70, 178, 128, 25, 70, 70, 94, 224, 54, 4, 54, 54, 25, 228, 160, 206, 165, 143, 206, 108, 220, 234, 160, 13, 169, 103, 103, 103, 91, 213, 222, 91, 103, 91, 103, 31, 30, 123, 13, 62, 103, 50, 106, 42, 13, 145, 114, 220, 65, 8, 8, 175, 11, 104, 94, 118, 132, 27, 118, 193, 27, 128, 127, 127, 183, 33, 30, 29, 103, 128, 61, 234, 165, 41, 29, 193, 33, 207, 41, 165, 165, 55, 81, 157, 157, 8, 81, 11, 27, 8, 8, 98, 96, 142, 145, 41, 179, 112, 62, 180, 206, 206, 165, 39, 241, 45, 151, 26, 197, 102, 192, 125, 128, 67, 128, 69, 128, 197, 33, 125, 102, 13, 103, 25, 30, 12, 30, 12, 30, 25, 77, 12, 25, 180, 27, 10, 69, 235, 228, 343, 118, 69, 41, 8, 69, 175, 25, 69, 25, 125, 41, 25, 41, 8, 155, 146, 155, 146, 155, 206, 168, 128, 157, 27, 273, 211, 211, 168, 11, 173, 154, 77, 173, 77, 102, 102, 102, 8, 85, 95, 102, 157, 28, 122, 234, 122, 157, 235, 222, 241, 10, 91, 179, 25, 13, 25, 41, 25, 206, 41, 6, 41, 158, 206, 206, 33, 296, 296, 33, 228, 69, 8, 114, 148, 33, 29, 66, 27, 27, 30, 233, 54, 173, 108, 106, 108, 108, 53, 103, 33, 33, 33, 176, 27, 27, 205, 164, 105, 237, 41, 27, 72, 165, 29, 29, 259, 132, 132, 132, 364, 71, 71, 27, 94, 160, 127, 51, 234, 55, 27, 95, 94, 165, 55, 55, 41, 0, 41, 128, 4, 123, 173, 6, 164, 157, 121, 121, 154, 86, 164, 164, 25, 93, 164, 25, 164, 210, 284, 62, 93, 30, 25, 25, 30, 30, 260, 130, 25, 125, 57, 53, 166, 166, 166, 185, 166, 158, 94, 113, 215, 159, 62, 99, 21, 172, 99, 184, 62, 259, 4, 21, 21, 77, 62, 173, 41, 146, 6, 41, 128, 121, 41, 11, 121, 103, 159, 164, 175, 206, 91, 103, 164, 72, 25, 129, 72, 206, 129, 33, 103, 102, 102, 29, 13, 11, 251, 234, 135, 31, 8, 123, 65, 91, 121, 129, 65, 243, 10, 91, 8, 65, 70, 228, 220, 243, 91, 10, 10, 30, 178, 91, 178, 33, 21, 25, 235, 165, 11, 161,
101, 8, 8, 98, 68, 155, 102, 132, 120, 30, 25, 123, 123, 101, 25, 123, 32, 24, 94, 145, 32, 24, 94, 118, 145, 101, 53, 53, 25, 128, 173, 142, 81, 81, 69, 33, 33, 125, 4, 1, 17, 27, 4, 17, 102, 27, 13, 25, 128, 71, 13, 39, 53, 13, 53, 47, 39, 23, 128, 53, 39, 47, 39, 135, 158, 136, 36, 36, 27, 157, 47, 76, 213, 47, 156, 25, 25, 53, 25, 53, 25, 86, 27, 159, 25, 62, 79, 39, 79, 25, 145, 49, 25, 143, 13, 114, 150, 130, 94, 102, 39, 4, 39, 61, 77, 228, 22, 25, 47, 119, 205, 122, 119, 205, 119, 22, 119, 258, 143, 22, 81, 179, 22, 22, 143, 25, 65, 53, 168, 36, 79, 175, 37, 79, 70, 79, 103, 70, 25, 175, 4, 96, 96, 49, 128, 138, 96, 22, 62, 47, 95, 105, 95, 62, 95, 62, 142, 103, 69, 103, 30, 103, 34, 173, 127, 70, 127, 132, 18, 85, 22, 71, 18, 206, 206, 18, 128, 145, 70, 193, 188, 8, 125, 114, 70, 128, 114, 145, 102, 25, 12, 108, 102, 94, 10, 102, 1, 102, 124, 22, 22, 118, 132, 22, 116, 75, 41, 63, 41, 189, 208, 55, 85, 69, 8, 71, 53, 71, 69, 102, 165, 41, 99, 69, 33, 33, 29, 156, 102, 13, 251, 102, 25, 13, 109, 102, 164, 102, 164, 102, 25, 29, 228, 29, 259, 179, 222, 95, 94, 30, 30, 30, 142, 55, 142, 72, 55, 102, 128, 17, 69, 164, 165, 3, 164, 36, 165, 27, 27, 45, 21, 21, 237, 113, 83, 231, 106, 13, 154, 13, 154, 128, 154, 148, 258, 25, 154, 128, 3, 27, 10, 145, 145, 21, 146, 25, 1, 185, 121, 0, 1, 95, 55, 95, 95, 30, 0, 27, 95, 0, 95, 8, 222, 27, 121, 30, 95, 121, 0, 98, 94, 131, 55, 95, 95, 30, 98, 30, 0, 91, 145, 66, 179, 66, 58, 175, 29, 0, 31, 173, 146, 160, 39, 53, 28, 123, 199, 123, 175, 146, 156, 54, 54, 149, 25, 70, 178, 128, 25, 70, 70, 94, 224, 54, 4, 54, 54, 25, 228, 160, 206, 165, 143, 206, 108, 220, 234, 160, 13, 169, 103, 103, 103, 91, 213, 222, 91, 103, 91, 103, 31, 30, 123, 13, 62, 103, 50, 106, 42, 13, 145, 114, 220, 65, 8, 8, 175, 11, 104, 94, 118, 132, 27, 118, 193, 27, 128, 127, 127, 183, 33, 30, 29, 103, 128, 61, 234, 165, 41, 29, 193, 33, 207, 41, 165, 165, 55, 81, 157, 157, 8, 81, 11, 27, 8, 8, 98, 96, 142, 145, 41, 179, 112, 62, 180, 206, 206, 165, 39, 241, 45, 151, 26, 197, 102, 192, 125, 128, 67, 128, 69, 128, 197, 33, 125, 102, 13, 103, 25, 30, 12, 30, 12, 30, 25, 77, 12, 25, 180, 27, 10, 69, 235, 228, 343, 118, 69, 41, 8, 69, 175, 25, 69, 25, 125, 41, 25, 41, 8, 155, 146, 155, 146, 155, 206, 168, 128, 157, 27, 273, 211, 211, 168, 11, 173, 154, 77, 173, 77, 102, 102, 102, 8, 85, 95, 102, 157, 28, 122, 234, 122, 157, 235, 222, 241, 10, 91, 179, 25, 13, 25, 41, 25, 206, 41, 6, 41, 158, 206, 206, 33, 296, 296, 33, 228, 69, 8, 114, 148, 33, 29, 66, 27, 27, 30, 233, 54, 173, 108, 106, 108, 108, 53, 103, 33, 33, 33, 176, 27, 27, 205, 164, 105, 237, 41, 27, 72, 165, 29, 29, 259, 132, 132, 132, 364, 71, 71, 27, 94, 160, 127, 51, 234, 55, 27, 95, 94, 165, 55, 55, 41, 0, 41, 128, 4, 123, 173, 6, 164, 157, 121, 121, 154, 86, 164, 164, 25, 93, 164, 25, 164, 210, 284, 62, 93, 30, 25, 25, 30, 30, 260, 130, 25, 125, 57, 53, 166, 166, 166, 185, 166, 158, 94, 113, 215, 159, 62, 99, 21, 172, 99, 184, 62, 259, 4, 21, 21, 77, 62, 173, 41, 146, 6, 41, 128, 121, 41, 11, 121, 103, 159, 164, 175, 206, 91, 103, 164, 72, 25, 129, 72, 206, 129, 33, 103, 102, 102, 29, 13, 11, 251, 234, 135, 31, 8, 123, 65, 91, 121, 129, 65, 243, 10, 91, 8, 65, 70, 228, 220, 243, 91, 10, 10, 30, 178, 91, 178, 33, 21, 25, 235, 165, 11, 161,
Luby, et al. Standards Track [Page 32] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[32ページ]。
158, 27, 27, 30, 128, 75, 36, 30, 36, 36, 173, 25, 33, 178, 112, 162, 112, 112, 112, 162, 33, 33, 178, 123, 123, 39, 106, 91, 106, 106, 158, 106, 106, 284, 39, 230, 21, 228, 11, 21, 228, 159, 241, 62, 10, 62, 10, 68, 234, 39, 39, 138, 62, 22, 27, 183, 22, 215, 10, 175, 175, 353, 228, 42, 193, 175, 175, 27, 98, 27, 193, 150, 27, 173, 17, 233, 233, 25, 102, 123, 152, 242, 108, 4, 94, 176, 13, 41, 219, 17, 151, 22, 103, 103, 53, 128, 233, 284, 25, 265, 128, 39, 39, 138, 42, 39, 21, 86, 95, 127, 29, 91, 46, 103, 103, 215, 25, 123, 123, 230, 25, 193, 180, 30, 60, 30, 242, 136, 180, 193, 30, 206, 180, 60, 165, 206, 193, 165, 123, 164, 103, 68, 25, 70, 91, 25, 82, 53, 82, 186, 53, 82, 53, 25, 30, 282, 91, 13, 234, 160, 160, 126, 149, 36, 36, 160, 149, 178, 160, 39, 294, 149, 149, 160, 39, 95, 221, 186, 106, 178, 316, 267, 53, 53, 164, 159, 164, 165, 94, 228, 53, 52, 178, 183, 53, 294, 128, 55, 140, 294, 25, 95, 366, 15, 304, 13, 183, 77, 230, 6, 136, 235, 121, 311, 273, 36, 158, 235, 230, 98, 201, 165, 165, 165, 91, 175, 248, 39, 185, 128, 39, 39, 128, 313, 91, 36, 219, 130, 25, 130, 234, 234, 130, 234, 121, 205, 304, 94, 77, 64, 259, 60, 60, 60, 77, 242, 60, 145, 95, 270, 18, 91, 199, 159, 91, 235, 58, 249, 26, 123, 114, 29, 15, 191, 15, 30, 55, 55, 347, 4, 29, 15, 4, 341, 93, 7, 30, 23, 7, 121, 266, 178, 261, 70, 169, 25, 25, 158, 169, 25, 169, 270, 270, 13, 128, 327, 103, 55, 128, 103, 136, 159, 103, 327, 41, 32, 111, 111, 114, 173, 215, 173, 25, 173, 180, 114, 173, 173, 98, 93, 25, 160, 157, 159, 160, 159, 159, 160, 320, 35, 193, 221, 33, 36, 136, 248, 91, 215, 125, 215, 156, 68, 125, 125, 1, 287, 123, 94, 30, 184, 13, 30, 94, 123, 206, 12, 206, 289, 128, 122, 184, 128, 289, 178, 29, 26, 206, 178, 65, 206, 128, 192, 102, 197, 36, 94, 94, 155, 10, 36, 121, 280, 121, 368, 192, 121, 121, 179, 121, 36, 54, 192, 121, 192, 197, 118, 123, 224, 118, 10, 192, 10, 91, 269, 91, 49, 206, 184, 185, 62, 8, 49, 289, 30, 5, 55, 30, 42, 39, 220, 298, 42, 347, 42, 234, 42, 70, 42, 55, 321, 129, 172, 173, 172, 13, 98, 129, 325, 235, 284, 362, 129, 233, 345, 175, 261, 175, 60, 261, 58, 289, 99, 99, 99, 206, 99, 36, 175, 29, 25, 432, 125, 264, 168, 173, 69, 158, 273, 179, 164, 69, 158, 69, 8, 95, 192, 30, 164, 101, 44, 53, 273, 335, 273, 53, 45, 128, 45, 234, 123, 105, 103, 103, 224, 36, 90, 211, 282, 264, 91, 228, 91, 166, 264, 228, 398, 50, 101, 91, 264, 73, 36, 25, 73, 50, 50, 242, 36, 36, 58, 165, 204, 353, 165, 125, 320, 128, 298, 298, 180, 128, 60, 102, 30, 30, 53, 179, 234, 325, 234, 175, 21, 250, 215, 103, 21, 21, 250, 91, 211, 91, 313, 301, 323, 215, 228, 160, 29, 29, 81, 53, 180, 146, 248, 66, 159, 39, 98, 323, 98, 36, 95, 218, 234, 39, 82, 82, 230, 62, 13, 62, 230, 13, 30, 98, 0, 8, 98, 8, 98, 91, 267, 121, 197, 30, 78, 27, 78, 102, 27, 298, 160, 103, 264, 264, 264, 175, 17, 273, 273, 165, 31, 160, 17, 99, 17, 99, 234, 31, 17, 99, 36, 26, 128, 29, 214, 353, 264, 102, 36, 102, 264, 264, 273, 273, 4, 16, 138, 138, 264, 128, 313, 25, 420, 60, 10, 280, 264, 60, 60, 103, 178, 125, 178, 29, 327, 29, 36, 30, 36, 4, 52, 183, 183, 173, 52, 31, 173, 31, 158, 31, 158, 31, 9, 31, 31, 353, 31, 353, 173, 415, 9, 17, 222, 31, 103, 31, 165, 27, 31, 31, 165, 27, 27, 206, 31, 31, 4, 4, 30, 4, 4, 264, 185, 159, 310, 273, 310, 173, 40, 4, 173, 4,
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Luby, et al. Standards Track [Page 33] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[33ページ]。
173, 4, 250, 250, 62, 188, 119, 250, 233, 62, 121, 105, 105, 54, 103, 111, 291, 236, 236, 103, 297, 36, 26, 316, 69, 183, 158, 206, 129, 160, 129, 184, 55, 179, 279, 11, 179, 347, 160, 184, 129, 179, 351, 179, 353, 179, 129, 129, 351, 11, 111, 93, 93, 235, 103, 173, 53, 93, 50, 111, 86, 123, 94, 36, 183, 60, 55, 55, 178, 219, 253, 321, 178, 235, 235, 183, 183, 204, 321, 219, 160, 193, 335, 121, 70, 69, 295, 159, 297, 231, 121, 231, 136, 353, 136, 121, 279, 215, 366, 215, 353, 159, 353, 353, 103, 31, 31, 298, 298, 30, 30, 165, 273, 25, 219, 35, 165, 259, 54, 36, 54, 54, 165, 71, 250, 327, 13, 289, 165, 196, 165, 165, 94, 233, 165, 94, 60, 165, 96, 220, 166, 271, 158, 397, 122, 53, 53, 137, 280, 272, 62, 30, 30, 30, 105, 102, 67, 140, 8, 67, 21, 270, 298, 69, 173, 298, 91, 179, 327, 86, 179, 88, 179, 179, 55, 123, 220, 233, 94, 94, 175, 13, 53, 13, 154, 191, 74, 83, 83, 325, 207, 83, 74, 83, 325, 74, 316, 388, 55, 55, 364, 55, 183, 434, 273, 273, 273, 164, 213, 11, 213, 327, 321, 21, 352, 185, 103, 13, 13, 55, 30, 323, 123, 178, 435, 178, 30, 175, 175, 30, 481, 527, 175, 125, 232, 306, 232, 206, 306, 364, 206, 270, 206, 232, 10, 30, 130, 160, 130, 347, 240, 30, 136, 130, 347, 136, 279, 298, 206, 30, 103, 273, 241, 70, 206, 306, 434, 206, 94, 94, 156, 161, 321, 321, 64, 161, 13, 183, 183, 83, 161, 13, 169, 13, 159, 36, 173, 159, 36, 36, 230, 235, 235, 159, 159, 335, 312, 42, 342, 264, 39, 39, 39, 34, 298, 36, 36, 252, 164, 29, 493, 29, 387, 387, 435, 493, 132, 273, 105, 132, 74, 73, 206, 234, 273, 206, 95, 15, 280, 280, 280, 280, 397, 273, 273, 242, 397, 280, 397, 397, 397, 273, 397, 280, 230, 137, 353, 67, 81, 137, 137, 353, 259, 312, 114, 164, 164, 25, 77, 21, 77, 165, 30, 30, 231, 234, 121, 234, 312, 121, 364, 136, 123, 123, 136, 123, 136, 150, 264, 285, 30, 166, 93, 30, 39, 224, 136, 39, 355, 355, 397, 67, 67, 25, 67, 25, 298, 11, 67, 264, 374, 99, 150, 321, 67, 70, 67, 295, 150, 29, 321, 150, 70, 29, 142, 355, 311, 173, 13, 253, 103, 114, 114, 70, 192, 22, 128, 128, 183, 184, 70, 77, 215, 102, 292, 30, 123, 279, 292, 142, 33, 215, 102, 468, 123, 468, 473, 30, 292, 215, 30, 213, 443, 473, 215, 234, 279, 279, 279, 279, 265, 443, 206, 66, 313, 34, 30, 206, 30, 51, 15, 206, 41, 434, 41, 398, 67, 30, 301, 67, 36, 3, 285, 437, 136, 136, 22, 136, 145, 365, 323, 323, 145, 136, 22, 453, 99, 323, 353, 9, 258, 323, 231, 128, 231, 382, 150, 420, 39, 94, 29, 29, 353, 22, 22, 347, 353, 39, 29, 22, 183, 8, 284, 355, 388, 284, 60, 64, 99, 60, 64, 150, 95, 150, 364, 150, 95, 150, 6, 236, 383, 544, 81, 206, 388, 206, 58, 159, 99, 231, 228, 363, 363, 121, 99, 121, 121, 99, 422, 544, 273, 173, 121, 427, 102, 121, 235, 284, 179, 25, 197, 25, 179, 511, 70, 368, 70, 25, 388, 123, 368, 159, 213, 410, 159, 236, 127, 159, 21, 373, 184, 424, 327, 250, 176, 176, 175, 284, 316, 176, 284, 327, 111, 250, 284, 175, 175, 264, 111, 176, 219, 111, 427, 427, 176, 284, 427, 353, 428, 55, 184, 493, 158, 136, 99, 287, 264, 334, 264, 213, 213, 292, 481, 93, 264, 292, 295, 295, 6, 367, 279, 173, 308, 285, 158, 308, 335, 299, 137, 137, 572, 41, 137, 137, 41, 94, 335, 220, 36, 224, 420, 36, 265, 265, 91, 91, 71, 123, 264, 91, 91, 123, 107, 30, 22, 292, 35, 241, 356, 298, 14, 298, 441, 35, 121, 71, 63, 130, 63, 488, 363, 71, 63, 307, 194, 71, 71, 220, 121, 125, 71,
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Luby, et al. Standards Track [Page 34] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[34ページ]。
220, 71, 71, 71, 71, 235, 265, 353, 128, 155, 128, 420, 400, 130, 173, 183, 183, 184, 130, 173, 183, 13, 183, 130, 130, 183, 183, 353, 353, 183, 242, 183, 183, 306, 324, 324, 321, 306, 321, 6, 6, 128, 306, 242, 242, 306, 183, 183, 6, 183, 321, 486, 183, 164, 30, 78, 138, 158, 138, 34, 206, 362, 55, 70, 67, 21, 375, 136, 298, 81, 298, 298, 298, 230, 121, 30, 230, 311, 240, 311, 311, 158, 204, 136, 136, 184, 136, 264, 311, 311, 312, 312, 72, 311, 175, 264, 91, 175, 264, 121, 461, 312, 312, 238, 475, 350, 512, 350, 312, 313, 350, 312, 366, 294, 30, 253, 253, 253, 388, 158, 388, 22, 388, 22, 388, 103, 321, 321, 253, 7, 437, 103, 114, 242, 114, 114, 242, 114, 114, 242, 242, 242, 306, 242, 114, 7, 353, 335, 27, 241, 299, 312, 364, 506, 409, 94, 462, 230, 462, 243, 230, 175, 175, 462, 461, 230, 428, 426, 175, 175, 165, 175, 175, 372, 183, 572, 102, 85, 102, 538, 206, 376, 85, 85, 284, 85, 85, 284, 398, 83, 160, 265, 308, 398, 310, 583, 289, 279, 273, 285, 490, 490, 211, 292, 292, 158, 398, 30, 220, 169, 368, 368, 368, 169, 159, 368, 93, 368, 368, 93, 169, 368, 368, 443, 368, 298, 443, 368, 298, 538, 345, 345, 311, 178, 54, 311, 215, 178, 175, 222, 264, 475, 264, 264, 475, 478, 289, 63, 236, 63, 299, 231, 296, 397, 299, 158, 36, 164, 164, 21, 492, 21, 164, 21, 164, 403, 26, 26, 588, 179, 234, 169, 465, 295, 67, 41, 353, 295, 538, 161, 185, 306, 323, 68, 420, 323, 82, 241, 241, 36, 53, 493, 301, 292, 241, 250, 63, 63, 103, 442, 353, 185, 353, 321, 353, 185, 353, 353, 185, 409, 353, 589, 34, 271, 271, 34, 86, 34, 34, 353, 353, 39, 414, 4, 95, 95, 4, 225, 95, 4, 121, 30, 552, 136, 159, 159, 514, 159, 159, 54, 514, 206, 136, 206, 159, 74, 235, 235, 312, 54, 312, 42, 156, 422, 629, 54, 465, 265, 165, 250, 35, 165, 175, 659, 175, 175, 8, 8, 8, 8, 206, 206, 206, 50, 435, 206, 432, 230, 230, 234, 230, 94, 299, 299, 285, 184, 41, 93, 299, 299, 285, 41, 285, 158, 285, 206, 299, 41, 36, 396, 364, 364, 120, 396, 514, 91, 382, 538, 807, 717, 22, 93, 412, 54, 215, 54, 298, 308, 148, 298, 148, 298, 308, 102, 656, 6, 148, 745, 128, 298, 64, 407, 273, 41, 172, 64, 234, 250, 398, 181, 445, 95, 236, 441, 477, 504, 102, 196, 137, 364, 60, 453, 137, 364, 367, 334, 364, 299, 196, 397, 630, 589, 589, 196, 646, 337, 235, 128, 128, 343, 289, 235, 324, 427, 324, 58, 215, 215, 461, 425, 461, 387, 440, 285, 440, 440, 285, 387, 632, 325, 325, 440, 461, 425, 425, 387, 627, 191, 285, 440, 308, 55, 219, 280, 308, 265, 538, 183, 121, 30, 236, 206, 30, 455, 236, 30, 30, 705, 83, 228, 280, 468, 132, 8, 132, 132, 128, 409, 173, 353, 132, 409, 35, 128, 450, 137, 398, 67, 432, 423, 235, 235, 388, 306, 93, 93, 452, 300, 190, 13, 452, 388, 30, 452, 13, 30, 13, 30, 306, 362, 234, 721, 635, 809, 784, 67, 498, 498, 67, 353, 635, 67, 183, 159, 445, 285, 183, 53, 183, 445, 265, 432, 57, 420, 432, 420, 477, 327, 55, 60, 105, 183, 218, 104, 104, 475, 239, 582, 151, 239, 104, 732, 41, 26, 784, 86, 300, 215, 36, 64, 86, 86, 675, 294, 64, 86, 528, 550, 493, 565, 298, 230, 312, 295, 538, 298, 295, 230, 54, 374, 516, 441, 54, 54, 323, 401, 401, 382, 159, 837, 159, 54, 401, 592, 159, 401, 417, 610, 264, 150, 323, 452, 185, 323, 323, 185, 403, 185, 423, 165, 425, 219, 407, 270, 231, 99, 93, 231, 631, 756, 71, 364, 434, 213, 86, 102, 434, 102, 86, 23, 71, 335, 164, 323,
220, 71, 71, 71, 71, 235, 265, 353, 128, 155, 128, 420, 400, 130, 173, 183, 183, 184, 130, 173, 183, 13, 183, 130, 130, 183, 183, 353, 353, 183, 242, 183, 183, 306, 324, 324, 321, 306, 321, 6, 6, 128, 306, 242, 242, 306, 183, 183, 6, 183, 321, 486, 183, 164, 30, 78, 138, 158, 138, 34, 206, 362, 55, 70, 67, 21, 375, 136, 298, 81, 298, 298, 298, 230, 121, 30, 230, 311, 240, 311, 311, 158, 204, 136, 136, 184, 136, 264, 311, 311, 312, 312, 72, 311, 175, 264, 91, 175, 264, 121, 461, 312, 312, 238, 475, 350, 512, 350, 312, 313, 350, 312, 366, 294, 30, 253, 253, 253, 388, 158, 388, 22, 388, 22, 388, 103, 321, 321, 253, 7, 437, 103, 114, 242, 114, 114, 242, 114, 114, 242, 242, 242, 306, 242, 114, 7, 353, 335, 27, 241, 299, 312, 364, 506, 409, 94, 462, 230, 462, 243, 230, 175, 175, 462, 461, 230, 428, 426, 175, 175, 165, 175, 175, 372, 183, 572, 102, 85, 102, 538, 206, 376, 85, 85, 284, 85, 85, 284, 398, 83, 160, 265, 308, 398, 310, 583, 289, 279, 273, 285, 490, 490, 211, 292, 292, 158, 398, 30, 220, 169, 368, 368, 368, 169, 159, 368, 93, 368, 368, 93, 169, 368, 368, 443, 368, 298, 443, 368, 298, 538, 345, 345, 311, 178, 54, 311, 215, 178, 175, 222, 264, 475, 264, 264, 475, 478, 289, 63, 236, 63, 299, 231, 296, 397, 299, 158, 36, 164, 164, 21, 492, 21, 164, 21, 164, 403, 26, 26, 588, 179, 234, 169, 465, 295, 67, 41, 353, 295, 538, 161, 185, 306, 323, 68, 420, 323, 82, 241, 241, 36, 53, 493, 301, 292, 241, 250, 63, 63, 103, 442, 353, 185, 353, 321, 353, 185, 353, 353, 185, 409, 353, 589, 34, 271, 271, 34, 86, 34, 34, 353, 353, 39, 414, 4, 95, 95, 4, 225, 95, 4, 121, 30, 552, 136, 159, 159, 514, 159, 159, 54, 514, 206, 136, 206, 159, 74, 235, 235, 312, 54, 312, 42, 156, 422, 629, 54, 465, 265, 165, 250, 35, 165, 175, 659, 175, 175, 8, 8, 8, 8, 206, 206, 206, 50, 435, 206, 432, 230, 230, 234, 230, 94, 299, 299, 285, 184, 41, 93, 299, 299, 285, 41, 285, 158, 285, 206, 299, 41, 36, 396, 364, 364, 120, 396, 514, 91, 382, 538, 807, 717, 22, 93, 412, 54, 215, 54, 298, 308, 148, 298, 148, 298, 308, 102, 656, 6, 148, 745, 128, 298, 64, 407, 273, 41, 172, 64, 234, 250, 398, 181, 445, 95, 236, 441, 477, 504, 102, 196, 137, 364, 60, 453, 137, 364, 367, 334, 364, 299, 196, 397, 630, 589, 589, 196, 646, 337, 235, 128, 128, 343, 289, 235, 324, 427, 324, 58, 215, 215, 461, 425, 461, 387, 440, 285, 440, 440, 285, 387, 632, 325, 325, 440, 461, 425, 425, 387, 627, 191, 285, 440, 308, 55, 219, 280, 308, 265, 538, 183, 121, 30, 236, 206, 30, 455, 236, 30, 30, 705, 83, 228, 280, 468, 132, 8, 132, 132, 128, 409, 173, 353, 132, 409, 35, 128, 450, 137, 398, 67, 432, 423, 235, 235, 388, 306, 93, 93, 452, 300, 190, 13, 452, 388, 30, 452, 13, 30, 13, 30, 306, 362, 234, 721, 635, 809, 784, 67, 498, 498, 67, 353, 635, 67, 183, 159, 445, 285, 183, 53, 183, 445, 265, 432, 57, 420, 432, 420, 477, 327, 55, 60, 105, 183, 218, 104, 104, 475, 239, 582, 151, 239, 104, 732, 41, 26, 784, 86, 300, 215, 36, 64, 86, 86, 675, 294, 64, 86, 528, 550, 493, 565, 298, 230, 312, 295, 538, 298, 295, 230, 54, 374, 516, 441, 54, 54, 323, 401, 401, 382, 159, 837, 159, 54, 401, 592, 159, 401, 417, 610, 264, 150, 323, 452, 185, 323, 323, 185, 403, 185, 423, 165, 425, 219, 407, 270, 231, 99, 93, 231, 631, 756, 71, 364, 434, 213, 86, 102, 434, 102, 86, 23, 71, 335, 164, 323,
Luby, et al. Standards Track [Page 35] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[35ページ]。
409, 381, 4, 124, 41, 424, 206, 41, 124, 41, 41, 703, 635, 124, 493, 41, 41, 487, 492, 124, 175, 124, 261, 600, 488, 261, 488, 261, 206, 677, 261, 308, 723, 908, 704, 691, 723, 488, 488, 441, 136, 476, 312, 136, 550, 572, 728, 550, 22, 312, 312, 22, 55, 413, 183, 280, 593, 191, 36, 36, 427, 36, 695, 592, 19, 544, 13, 468, 13, 544, 72, 437, 321, 266, 461, 266, 441, 230, 409, 93, 521, 521, 345, 235, 22, 142, 150, 102, 569, 235, 264, 91, 521, 264, 7, 102, 7, 498, 521, 235, 537, 235, 6, 241, 420, 420, 631, 41, 527, 103, 67, 337, 62, 264, 527, 131, 67, 174, 263, 264, 36, 36, 263, 581, 253, 465, 160, 286, 91, 160, 55, 4, 4, 631, 631, 608, 365, 465, 294, 427, 427, 335, 669, 669, 129, 93, 93, 93, 93, 74, 66, 758, 504, 347, 130, 505, 504, 143, 505, 550, 222, 13, 352, 529, 291, 538, 50, 68, 269, 130, 295, 130, 511, 295, 295, 130, 486, 132, 61, 206, 185, 368, 669, 22, 175, 492, 207, 373, 452, 432, 327, 89, 550, 496, 611, 527, 89, 527, 496, 550, 516, 516, 91, 136, 538, 264, 264, 124, 264, 264, 264, 264, 264, 535, 264, 150, 285, 398, 285, 582, 398, 475, 81, 694, 694, 64, 81, 694, 234, 607, 723, 513, 234, 64, 581, 64, 124, 64, 607, 234, 723, 717, 367, 64, 513, 607, 488, 183, 488, 450, 183, 550, 286, 183, 363, 286, 414, 67, 449, 449, 366, 215, 235, 95, 295, 295, 41, 335, 21, 445, 225, 21, 295, 372, 749, 461, 53, 481, 397, 427, 427, 427, 714, 481, 714, 427, 717, 165, 245, 486, 415, 245, 415, 486, 274, 415, 441, 456, 300, 548, 300, 422, 422, 757, 11, 74, 430, 430, 136, 409, 430, 749, 191, 819, 592, 136, 364, 465, 231, 231, 918, 160, 589, 160, 160, 465, 465, 231, 157, 538, 538, 259, 538, 326, 22, 22, 22, 179, 22, 22, 550, 179, 287, 287, 417, 327, 498, 498, 287, 488, 327, 538, 488, 583, 488, 287, 335, 287, 335, 287, 41, 287, 335, 287, 327, 441, 335, 287, 488, 538, 327, 498, 8, 8, 374, 8, 64, 427, 8, 374, 417, 760, 409, 373, 160, 423, 206, 160, 106, 499, 160, 271, 235, 160, 590, 353, 695, 478, 619, 590, 353, 13, 63, 189, 420, 605, 427, 643, 121, 280, 415, 121, 415, 595, 417, 121, 398, 55, 330, 463, 463, 123, 353, 330, 582, 309, 582, 582, 405, 330, 550, 405, 582, 353, 309, 308, 60, 353, 7, 60, 71, 353, 189, 183, 183, 183, 582, 755, 189, 437, 287, 189, 183, 668, 481, 384, 384, 481, 481, 481, 477, 582, 582, 499, 650, 481, 121, 461, 231, 36, 235, 36, 413, 235, 209, 36, 689, 114, 353, 353, 235, 592, 36, 353, 413, 209, 70, 308, 70, 699, 308, 70, 213, 292, 86, 689, 465, 55, 508, 128, 452, 29, 41, 681, 573, 352, 21, 21, 648, 648, 69, 509, 409, 21, 264, 21, 509, 514, 514, 409, 21, 264, 443, 443, 427, 160, 433, 663, 433, 231, 646, 185, 482, 646, 433, 13, 398, 172, 234, 42, 491, 172, 234, 234, 832, 775, 172, 196, 335, 822, 461, 298, 461, 364, 1120, 537, 169, 169, 364, 694, 219, 612, 231, 740, 42, 235, 321, 279, 960, 279, 353, 492, 159, 572, 321, 159, 287, 353, 287, 287, 206, 206, 321, 287, 159, 321, 492, 159, 55, 572, 600, 270, 492, 784, 173, 91, 91, 443, 443, 582, 261, 497, 572, 91, 555, 352, 206, 261, 555, 285, 91, 555, 497, 83, 91, 619, 353, 488, 112, 4, 592, 295, 295, 488, 235, 231, 769, 568, 581, 671, 451, 451, 483, 299, 1011, 432, 422, 207, 106, 701, 508, 555, 508, 555, 125, 870, 555, 589, 508, 125, 749, 482, 125, 125, 130, 544, 643, 643, 544, 488, 22, 643, 130, 335, 544, 22, 130, 544, 544, 488, 426, 426, 4, 180, 4, 695, 35, 54, 433, 500, 592, 433, 262,
409, 381, 4, 124, 41, 424, 206, 41, 124, 41, 41, 703, 635, 124, 493, 41, 41, 487, 492, 124, 175, 124, 261, 600, 488, 261, 488, 261, 206, 677, 261, 308, 723, 908, 704, 691, 723, 488, 488, 441, 136, 476, 312, 136, 550, 572, 728, 550, 22, 312, 312, 22, 55, 413, 183, 280, 593, 191, 36, 36, 427, 36, 695, 592, 19, 544, 13, 468, 13, 544, 72, 437, 321, 266, 461, 266, 441, 230, 409, 93, 521, 521, 345, 235, 22, 142, 150, 102, 569, 235, 264, 91, 521, 264, 7, 102, 7, 498, 521, 235, 537, 235, 6, 241, 420, 420, 631, 41, 527, 103, 67, 337, 62, 264, 527, 131, 67, 174, 263, 264, 36, 36, 263, 581, 253, 465, 160, 286, 91, 160, 55, 4, 4, 631, 631, 608, 365, 465, 294, 427, 427, 335, 669, 669, 129, 93, 93, 93, 93, 74, 66, 758, 504, 347, 130, 505, 504, 143, 505, 550, 222, 13, 352, 529, 291, 538, 50, 68, 269, 130, 295, 130, 511, 295, 295, 130, 486, 132, 61, 206, 185, 368, 669, 22, 175, 492, 207, 373, 452, 432, 327, 89, 550, 496, 611, 527, 89, 527, 496, 550, 516, 516, 91, 136, 538, 264, 264, 124, 264, 264, 264, 264, 264, 535, 264, 150, 285, 398, 285, 582, 398, 475, 81, 694, 694, 64, 81, 694, 234, 607, 723, 513, 234, 64, 581, 64, 124, 64, 607, 234, 723, 717, 367, 64, 513, 607, 488, 183, 488, 450, 183, 550, 286, 183, 363, 286, 414, 67, 449, 449, 366, 215, 235, 95, 295, 295, 41, 335, 21, 445, 225, 21, 295, 372, 749, 461, 53, 481, 397, 427, 427, 427, 714, 481, 714, 427, 717, 165, 245, 486, 415, 245, 415, 486, 274, 415, 441, 456, 300, 548, 300, 422, 422, 757, 11, 74, 430, 430, 136, 409, 430, 749, 191, 819, 592, 136, 364, 465, 231, 231, 918, 160, 589, 160, 160, 465, 465, 231, 157, 538, 538, 259, 538, 326, 22, 22, 22, 179, 22, 22, 550, 179, 287, 287, 417, 327, 498, 498, 287, 488, 327, 538, 488, 583, 488, 287, 335, 287, 335, 287, 41, 287, 335, 287, 327, 441, 335, 287, 488, 538, 327, 498, 8, 8, 374, 8, 64, 427, 8, 374, 417, 760, 409, 373, 160, 423, 206, 160, 106, 499, 160, 271, 235, 160, 590, 353, 695, 478, 619, 590, 353, 13, 63, 189, 420, 605, 427, 643, 121, 280, 415, 121, 415, 595, 417, 121, 398, 55, 330, 463, 463, 123, 353, 330, 582, 309, 582, 582, 405, 330, 550, 405, 582, 353, 309, 308, 60, 353, 7, 60, 71, 353, 189, 183, 183, 183, 582, 755, 189, 437, 287, 189, 183, 668, 481, 384, 384, 481, 481, 481, 477, 582, 582, 499, 650, 481, 121, 461, 231, 36, 235, 36, 413, 235, 209, 36, 689, 114, 353, 353, 235, 592, 36, 353, 413, 209, 70, 308, 70, 699, 308, 70, 213, 292, 86, 689, 465, 55, 508, 128, 452, 29, 41, 681, 573, 352, 21, 21, 648, 648, 69, 509, 409, 21, 264, 21, 509, 514, 514, 409, 21, 264, 443, 443, 427, 160, 433, 663, 433, 231, 646, 185, 482, 646, 433, 13, 398, 172, 234, 42, 491, 172, 234, 234, 832, 775, 172, 196, 335, 822, 461, 298, 461, 364, 1120, 537, 169, 169, 364, 694, 219, 612, 231, 740, 42, 235, 321, 279, 960, 279, 353, 492, 159, 572, 321, 159, 287, 353, 287, 287, 206, 206, 321, 287, 159, 321, 492, 159, 55, 572, 600, 270, 492, 784, 173, 91, 91, 443, 443, 582, 261, 497, 572, 91, 555, 352, 206, 261, 555, 285, 91, 555, 497, 83, 91, 619, 353, 488, 112, 4, 592, 295, 295, 488, 235, 231, 769, 568, 581, 671, 451, 451, 483, 299, 1011, 432, 422, 207, 106, 701, 508, 555, 508, 555, 125, 870, 555, 589, 508, 125, 749, 482, 125, 125, 130, 544, 643, 643, 544, 488, 22, 643, 130, 335, 544, 22, 130, 544, 544, 488, 426, 426, 4, 180, 4, 695, 35, 54, 433, 500, 592, 433, 262,
Luby, et al. Standards Track [Page 36] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[36ページ]。
94, 401, 401, 106, 216, 216, 106, 521, 102, 462, 518, 271, 475, 365, 193, 648, 206, 424, 206, 193, 206, 206, 424, 299, 590, 590, 364, 621, 67, 538, 488, 567, 51, 51, 513, 194, 81, 488, 486, 289, 567, 563, 749, 563, 338, 338, 502, 563, 822, 338, 563, 338, 502, 201, 230, 201, 533, 445, 175, 201, 175, 13, 85, 960, 103, 85, 175, 30, 445, 445, 175, 573, 196, 877, 287, 356, 678, 235, 489, 312, 572, 264, 717, 138, 295, 6, 295, 523, 55, 165, 165, 295, 138, 663, 6, 295, 6, 353, 138, 6, 138, 169, 129, 784, 12, 129, 194, 605, 784, 445, 234, 627, 563, 689, 627, 647, 570, 627, 570, 647, 206, 234, 215, 234, 816, 627, 816, 234, 627, 215, 234, 627, 264, 427, 427, 30, 424, 161, 161, 916, 740, 180, 616, 481, 514, 383, 265, 481, 164, 650, 121, 582, 689, 420, 669, 589, 420, 788, 549, 165, 734, 280, 224, 146, 681, 788, 184, 398, 784, 4, 398, 417, 417, 398, 636, 784, 417, 81, 398, 417, 81, 185, 827, 420, 241, 420, 41, 185, 185, 718, 241, 101, 185, 185, 241, 241, 241, 241, 241, 185, 324, 420, 420, 1011, 420, 827, 241, 184, 563, 241, 183, 285, 529, 285, 808, 822, 891, 822, 488, 285, 486, 619, 55, 869, 39, 567, 39, 289, 203, 158, 289, 710, 818, 158, 818, 355, 29, 409, 203, 308, 648, 792, 308, 308, 91, 308, 6, 592, 792, 106, 106, 308, 41, 178, 91, 751, 91, 259, 734, 166, 36, 327, 166, 230, 205, 205, 172, 128, 230, 432, 623, 838, 623, 432, 278, 432, 42, 916, 432, 694, 623, 352, 452, 93, 314, 93, 93, 641, 88, 970, 914, 230, 61, 159, 270, 159, 493, 159, 755, 159, 409, 30, 30, 836, 128, 241, 99, 102, 984, 538, 102, 102, 273, 639, 838, 102, 102, 136, 637, 508, 627, 285, 465, 327, 327, 21, 749, 327, 749, 21, 845, 21, 21, 409, 749, 1367, 806, 616, 714, 253, 616, 714, 714, 112, 375, 21, 112, 375, 375, 51, 51, 51, 51, 393, 206, 870, 713, 193, 802, 21, 1061, 42, 382, 42, 543, 876, 42, 876, 382, 696, 543, 635, 490, 353, 353, 417, 64, 1257, 271, 64, 377, 127, 127, 537, 417, 905, 353, 538, 465, 605, 876, 427, 324, 514, 852, 427, 53, 427, 557, 173, 173, 7, 1274, 563, 31, 31, 31, 745, 392, 289, 230, 230, 230, 91, 218, 327, 420, 420, 128, 901, 552, 420, 230, 608, 552, 476, 347, 476, 231, 159, 137, 716, 648, 716, 627, 740, 718, 679, 679, 6, 718, 740, 6, 189, 679, 125, 159, 757, 1191, 409, 175, 250, 409, 67, 324, 681, 605, 550, 398, 550, 931, 478, 174, 21, 316, 91, 316, 654, 409, 425, 425, 699, 61, 699, 321, 698, 321, 698, 61, 425, 699, 321, 409, 699, 299, 335, 321, 335, 61, 698, 699, 654, 698, 299, 425, 231, 14, 121, 515, 121, 14, 165, 81, 409, 189, 81, 373, 465, 463, 1055, 507, 81, 81, 189, 1246, 321, 409, 886, 104, 842, 689, 300, 740, 380, 656, 656, 832, 656, 380, 300, 300, 206, 187, 175, 142, 465, 206, 271, 468, 215, 560, 83, 215, 83, 215, 215, 83, 175, 215, 83, 83, 111, 206, 756, 559, 756, 1367, 206, 559, 1015, 559, 559, 946, 1015, 548, 559, 756, 1043, 756, 698, 159, 414, 308, 458, 997, 663, 663, 347, 39, 755, 838, 323, 755, 323, 159, 159, 717, 159, 21, 41, 128, 516, 159, 717, 71, 870, 755, 159, 740, 717, 374, 516, 740, 51, 148, 335, 148, 335, 791, 120, 364, 335, 335, 51, 120, 251, 538, 251, 971, 1395, 538, 78, 178, 538, 538, 918, 129, 918, 129, 538, 538, 656, 129, 538, 538, 129, 538, 1051, 538, 128, 838, 931, 998, 823, 1095, 334, 870, 334, 367, 550, 1061, 498, 745, 832, 498, 745, 716, 498, 498, 128, 997, 832, 716, 832, 130, 642, 616, 497, 432, 432, 432,
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Luby, et al. Standards Track [Page 37] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[37ページ]。
432, 642, 159, 432, 46, 230, 788, 160, 230, 478, 46, 693, 103, 920, 230, 589, 643, 160, 616, 432, 165, 165, 583, 592, 838, 784, 583, 710, 6, 583, 583, 6, 35, 230, 838, 592, 710, 6, 589, 230, 838, 30, 592, 583, 6, 583, 6, 6, 583, 30, 30, 6, 375, 375, 99, 36, 1158, 425, 662, 417, 681, 364, 375, 1025, 538, 822, 669, 893, 538, 538, 450, 409, 632, 527, 632, 563, 632, 527, 550, 71, 698, 550, 39, 550, 514, 537, 514, 537, 111, 41, 173, 592, 173, 648, 173, 173, 173, 1011, 514, 173, 173, 514, 166, 648, 355, 161, 166, 648, 497, 327, 327, 550, 650, 21, 425, 605, 555, 103, 425, 605, 842, 836, 1011, 636, 138, 756, 836, 756, 756, 353, 1011, 636, 636, 1158, 741, 741, 842, 756, 741, 1011, 677, 1011, 770, 366, 306, 488, 920, 920, 665, 775, 502, 500, 775, 775, 648, 364, 833, 207, 13, 93, 500, 364, 500, 665, 500, 93, 295, 183, 1293, 313, 272, 313, 279, 303, 93, 516, 93, 1013, 381, 6, 93, 93, 303, 259, 643, 168, 673, 230, 1261, 230, 230, 673, 1060, 1079, 1079, 550, 741, 741, 590, 527, 741, 741, 442, 741, 442, 848, 741, 590, 925, 219, 527, 925, 335, 442, 590, 239, 590, 590, 590, 239, 527, 239, 1033, 230, 734, 241, 741, 230, 549, 548, 1015, 1015, 32, 36, 433, 465, 724, 465, 73, 73, 73, 465, 808, 73, 592, 1430, 250, 154, 154, 250, 538, 353, 353, 353, 353, 353, 175, 194, 206, 538, 632, 1163, 960, 175, 175, 538, 452, 632, 1163, 175, 538, 960, 194, 175, 194, 632, 960, 632, 94, 632, 461, 960, 1163, 1163, 461, 632, 960, 755, 707, 105, 382, 625, 382, 382, 784, 707, 871, 559, 387, 387, 871, 784, 559, 784, 88, 36, 570, 314, 1028, 975, 335, 335, 398, 573, 573, 573, 21, 215, 562, 738, 612, 424, 21, 103, 788, 870, 912, 23, 186, 757, 73, 818, 23, 73, 563, 952, 262, 563, 137, 262, 1022, 952, 137, 1273, 442, 952, 604, 137, 308, 384, 913, 235, 325, 695, 398, 95, 668, 776, 713, 309, 691, 22, 10, 364, 682, 682, 578, 481, 1252, 1072, 1252, 825, 578, 825, 1072, 1149, 592, 273, 387, 273, 427, 155, 1204, 50, 452, 50, 1142, 50, 367, 452, 1142, 611, 367, 50, 50, 367, 50, 1675, 99, 367, 50, 1501, 1099, 830, 681, 689, 917, 1089, 453, 425, 235, 918, 538, 550, 335, 161, 387, 859, 324, 21, 838, 859, 1123, 21, 723, 21, 335, 335, 206, 21, 364, 1426, 21, 838, 838, 335, 364, 21, 21, 859, 920, 838, 838, 397, 81, 639, 397, 397, 588, 933, 933, 784, 222, 830, 36, 36, 222, 1251, 266, 36, 146, 266, 366, 581, 605, 366, 22, 966, 681, 681, 433, 730, 1013, 550, 21, 21, 938, 488, 516, 21, 21, 656, 420, 323, 323, 323, 327, 323, 918, 581, 581, 830, 361, 830, 364, 259, 364, 496, 496, 364, 691, 705, 691, 475, 427, 1145, 600, 179, 427, 527, 749, 869, 689, 335, 347, 220, 298, 689, 1426, 183, 554, 55, 832, 550, 550, 165, 770, 957, 67, 1386, 219, 683, 683, 355, 683, 355, 355, 738, 355, 842, 931, 266, 325, 349, 256, 1113, 256, 423, 960, 554, 554, 325, 554, 508, 22, 142, 22, 508, 916, 767, 55, 1529, 767, 55, 1286, 93, 972, 550, 931, 1286, 1286, 972, 93, 1286, 1392, 890, 93, 1286, 93, 1286, 972, 374, 931, 890, 808, 779, 975, 975, 175, 173, 4, 681, 383, 1367, 173, 383, 1367, 383, 173, 175, 69, 238, 146, 238, 36, 148, 888, 238, 173, 238, 148, 238, 888, 185, 925, 925, 797, 925, 815, 925, 469, 784, 289, 784, 925, 797, 925, 925, 1093, 925, 925, 925, 1163, 797, 797, 815, 925, 1093, 784, 636, 663, 925, 187, 922, 316, 1380, 709, 916, 916, 187, 355, 948, 916, 187,
432, 642, 159, 432, 46, 230, 788, 160, 230, 478, 46, 693, 103, 920, 230, 589, 643, 160, 616, 432, 165, 165, 583, 592, 838, 784, 583, 710, 6, 583, 583, 6, 35, 230, 838, 592, 710, 6, 589, 230, 838, 30, 592, 583, 6, 583, 6, 6, 583, 30, 30, 6, 375, 375, 99, 36, 1158, 425, 662, 417, 681, 364, 375, 1025, 538, 822, 669, 893, 538, 538, 450, 409, 632, 527, 632, 563, 632, 527, 550, 71, 698, 550, 39, 550, 514, 537, 514, 537, 111, 41, 173, 592, 173, 648, 173, 173, 173, 1011, 514, 173, 173, 514, 166, 648, 355, 161, 166, 648, 497, 327, 327, 550, 650, 21, 425, 605, 555, 103, 425, 605, 842, 836, 1011, 636, 138, 756, 836, 756, 756, 353, 1011, 636, 636, 1158, 741, 741, 842, 756, 741, 1011, 677, 1011, 770, 366, 306, 488, 920, 920, 665, 775, 502, 500, 775, 775, 648, 364, 833, 207, 13, 93, 500, 364, 500, 665, 500, 93, 295, 183, 1293, 313, 272, 313, 279, 303, 93, 516, 93, 1013, 381, 6, 93, 93, 303, 259, 643, 168, 673, 230, 1261, 230, 230, 673, 1060, 1079, 1079, 550, 741, 741, 590, 527, 741, 741, 442, 741, 442, 848, 741, 590, 925, 219, 527, 925, 335, 442, 590, 239, 590, 590, 590, 239, 527, 239, 1033, 230, 734, 241, 741, 230, 549, 548, 1015, 1015, 32, 36, 433, 465, 724, 465, 73, 73, 73, 465, 808, 73, 592, 1430, 250, 154, 154, 250, 538, 353, 353, 353, 353, 353, 175, 194, 206, 538, 632, 1163, 960, 175, 175, 538, 452, 632, 1163, 175, 538, 960, 194, 175, 194, 632, 960, 632, 94, 632, 461, 960, 1163, 1163, 461, 632, 960, 755, 707, 105, 382, 625, 382, 382, 784, 707, 871, 559, 387, 387, 871, 784, 559, 784, 88, 36, 570, 314, 1028, 975, 335, 335, 398, 573, 573, 573, 21, 215, 562, 738, 612, 424, 21, 103, 788, 870, 912, 23, 186, 757, 73, 818, 23, 73, 563, 952, 262, 563, 137, 262, 1022, 952, 137, 1273, 442, 952, 604, 137, 308, 384, 913, 235, 325, 695, 398, 95, 668, 776, 713, 309, 691, 22, 10, 364, 682, 682, 578, 481, 1252, 1072, 1252, 825, 578, 825, 1072, 1149, 592, 273, 387, 273, 427, 155, 1204, 50, 452, 50, 1142, 50, 367, 452, 1142, 611, 367, 50, 50, 367, 50, 1675, 99, 367, 50, 1501, 1099, 830, 681, 689, 917, 1089, 453, 425, 235, 918, 538, 550, 335, 161, 387, 859, 324, 21, 838, 859, 1123, 21, 723, 21, 335, 335, 206, 21, 364, 1426, 21, 838, 838, 335, 364, 21, 21, 859, 920, 838, 838, 397, 81, 639, 397, 397, 588, 933, 933, 784, 222, 830, 36, 36, 222, 1251, 266, 36, 146, 266, 366, 581, 605, 366, 22, 966, 681, 681, 433, 730, 1013, 550, 21, 21, 938, 488, 516, 21, 21, 656, 420, 323, 323, 323, 327, 323, 918, 581, 581, 830, 361, 830, 364, 259, 364, 496, 496, 364, 691, 705, 691, 475, 427, 1145, 600, 179, 427, 527, 749, 869, 689, 335, 347, 220, 298, 689, 1426, 183, 554, 55, 832, 550, 550, 165, 770, 957, 67, 1386, 219, 683, 683, 355, 683, 355, 355, 738, 355, 842, 931, 266, 325, 349, 256, 1113, 256, 423, 960, 554, 554, 325, 554, 508, 22, 142, 22, 508, 916, 767, 55, 1529, 767, 55, 1286, 93, 972, 550, 931, 1286, 1286, 972, 93, 1286, 1392, 890, 93, 1286, 93, 1286, 972, 374, 931, 890, 808, 779, 975, 975, 175, 173, 4, 681, 383, 1367, 173, 383, 1367, 383, 173, 175, 69, 238, 146, 238, 36, 148, 888, 238, 173, 238, 148, 238, 888, 185, 925, 925, 797, 925, 815, 925, 469, 784, 289, 784, 925, 797, 925, 925, 1093, 925, 925, 925, 1163, 797, 797, 815, 925, 1093, 784, 636, 663, 925, 187, 922, 316, 1380, 709, 916, 916, 187, 355, 948, 916, 187,
Luby, et al. Standards Track [Page 38] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[38ページ]。
916, 916, 948, 948, 916, 355, 316, 316, 334, 300, 1461, 36, 583, 1179, 699, 235, 858, 583, 699, 858, 699, 1189, 1256, 1189, 699, 797, 699, 699, 699, 699, 427, 488, 427, 488, 175, 815, 656, 656, 150, 322, 465, 322, 870, 465, 1099, 582, 665, 767, 749, 635, 749, 600, 1448, 36, 502, 235, 502, 355, 502, 355, 355, 355, 172, 355, 355, 95, 866, 425, 393, 1165, 42, 42, 42, 393, 939, 909, 909, 836, 552, 424, 1333, 852, 897, 1426, 1333, 1446, 1426, 997, 1011, 852, 1198, 55, 32, 239, 588, 681, 681, 239, 1401, 32, 588, 239, 462, 286, 1260, 984, 1160, 960, 960, 486, 828, 462, 960, 1199, 581, 850, 663, 581, 751, 581, 581, 1571, 252, 252, 1283, 264, 430, 264, 430, 430, 842, 252, 745, 21, 307, 681, 1592, 488, 857, 857, 1161, 857, 857, 857, 138, 374, 374, 1196, 374, 1903, 1782, 1626, 414, 112, 1477, 1040, 356, 775, 414, 414, 112, 356, 775, 435, 338, 1066, 689, 689, 1501, 689, 1249, 205, 689, 765, 220, 308, 917, 308, 308, 220, 327, 387, 838, 917, 917, 917, 220, 662, 308, 220, 387, 387, 220, 220, 308, 308, 308, 387, 1009, 1745, 822, 279, 554, 1129, 543, 383, 870, 1425, 241, 870, 241, 383, 716, 592, 21, 21, 592, 425, 550, 550, 550, 427, 230, 57, 483, 784, 860, 57, 308, 57, 486, 870, 447, 486, 433, 433, 870, 433, 997, 486, 443, 433, 433, 997, 486, 1292, 47, 708, 81, 895, 394, 81, 935, 81, 81, 81, 374, 986, 916, 1103, 1095, 465, 495, 916, 667, 1745, 518, 220, 1338, 220, 734, 1294, 741, 166, 828, 741, 741, 1165, 1371, 1371, 471, 1371, 647, 1142, 1878, 1878, 1371, 1371, 822, 66, 327, 158, 427, 427, 465, 465, 676, 676, 30, 30, 676, 676, 893, 1592, 93, 455, 308, 582, 695, 582, 629, 582, 85, 1179, 85, 85, 1592, 1179, 280, 1027, 681, 398, 1027, 398, 295, 784, 740, 509, 425, 968, 509, 46, 833, 842, 401, 184, 401, 464, 6, 1501, 1501, 550, 538, 883, 538, 883, 883, 883, 1129, 550, 550, 333, 689, 948, 21, 21, 241, 2557, 2094, 273, 308, 58, 863, 893, 1086, 409, 136, 1086, 592, 592, 830, 830, 883, 830, 277, 68, 689, 902, 277, 453, 507, 129, 689, 630, 664, 550, 128, 1626, 1626, 128, 902, 312, 589, 755, 755, 589, 755, 407, 1782, 589, 784, 1516, 1118, 407, 407, 1447, 589, 235, 755, 1191, 235, 235, 407, 128, 589, 1118, 21, 383, 1331, 691, 481, 383, 1129, 1129, 1261, 1104, 1378, 1129, 784, 1129, 1261, 1129, 947, 1129, 784, 784, 1129, 1129, 35, 1104, 35, 866, 1129, 1129, 64, 481, 730, 1260, 481, 970, 481, 481, 481, 481, 863, 481, 681, 699, 863, 486, 681, 481, 481, 55, 55, 235, 1364, 944, 632, 822, 401, 822, 952, 822, 822, 99, 550, 2240, 550, 70, 891, 860, 860, 550, 550, 916, 1176, 1530, 425, 1530, 916, 628, 1583, 916, 628, 916, 916, 628, 628, 425, 916, 1062, 1265, 916, 916, 916, 280, 461, 916, 916, 1583, 628, 1062, 916, 916, 677, 1297, 924, 1260, 83, 1260, 482, 433, 234, 462, 323, 1656, 997, 323, 323, 931, 838, 931, 1933, 1391, 367, 323, 931, 1391, 1391, 103, 1116, 1116, 1116, 769, 1195, 1218, 312, 791, 312, 741, 791, 997, 312, 334, 334, 312, 287, 287, 633, 1397, 1426, 605, 1431, 327, 592, 705, 1194, 592, 1097, 1118, 1503, 1267, 1267, 1267, 618, 1229, 734, 1089, 785, 1089, 1129, 1148, 1148, 1089, 915, 1148, 1129, 1148, 1011, 1011, 1229, 871, 1560, 1560, 1560, 563, 1537, 1009, 1560, 632, 985, 592, 1308, 592, 882, 145, 145, 397, 837, 383, 592, 592, 832, 36, 2714, 2107, 1588, 1347, 36, 36, 1443, 1453, 334, 2230, 1588, 1169, 650,
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Luby, et al. Standards Track [Page 39] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[39ページ]。
1169, 2107, 425, 425, 891, 891, 425, 2532, 679, 274, 274, 274, 325, 274, 1297, 194, 1297, 627, 314, 917, 314, 314, 1501, 414, 1490, 1036, 592, 1036, 1025, 901, 1218, 1025, 901, 280, 592, 592, 901, 1461, 159, 159, 159, 2076, 1066, 1176, 1176, 516, 327, 516, 1179, 1176, 899, 1176, 1176, 323, 1187, 1229, 663, 1229, 504, 1229, 916, 1229, 916, 1661, 41, 36, 278, 1027, 648, 648, 648, 1626, 648, 646, 1179, 1580, 1061, 1514, 1008, 1741, 2076, 1514, 1008, 952, 1089, 427, 952, 427, 1083, 425, 427, 1089, 1083, 425, 427, 425, 230, 920, 1678, 920, 1678, 189, 189, 953, 189, 133, 189, 1075, 189, 189, 133, 1264, 725, 189, 1629, 189, 808, 230, 230, 2179, 770, 230, 770, 230, 21, 21, 784, 1118, 230, 230, 230, 770, 1118, 986, 808, 916, 30, 327, 918, 679, 414, 916, 1165, 1355, 916, 755, 733, 433, 1490, 433, 433, 433, 605, 433, 433, 433, 1446, 679, 206, 433, 21, 2452, 206, 206, 433, 1894, 206, 822, 206, 2073, 206, 206, 21, 822, 21, 206, 206, 21, 383, 1513, 375, 1347, 432, 1589, 172, 954, 242, 1256, 1256, 1248, 1256, 1256, 1248, 1248, 1256, 842, 13, 592, 13, 842, 1291, 592, 21, 175, 13, 592, 13, 13, 1426, 13, 1541, 445, 808, 808, 863, 647, 219, 1592, 1029, 1225, 917, 1963, 1129, 555, 1313, 550, 660, 550, 220, 660, 552, 663, 220, 533, 220, 383, 550, 1278, 1495, 636, 842, 1036, 425, 842, 425, 1537, 1278, 842, 554, 1508, 636, 554, 301, 842, 792, 1392, 1021, 284, 1172, 997, 1021, 103, 1316, 308, 1210, 848, 848, 1089, 1089, 848, 848, 67, 1029, 827, 1029, 2078, 827, 1312, 1029, 827, 590, 872, 1312, 427, 67, 67, 67, 67, 872, 827, 872, 2126, 1436, 26, 2126, 67, 1072, 2126, 1610, 872, 1620, 883, 883, 1397, 1189, 555, 555, 563, 1189, 555, 640, 555, 640, 1089, 1089, 610, 610, 1585, 610, 1355, 610, 1015, 616, 925, 1015, 482, 230, 707, 231, 888, 1355, 589, 1379, 151, 931, 1486, 1486, 393, 235, 960, 590, 235, 960, 422, 142, 285, 285, 327, 327, 442, 2009, 822, 445, 822, 567, 888, 2611, 1537, 323, 55, 1537, 323, 888, 2611, 323, 1537, 323, 58, 445, 593, 2045, 593, 58, 47, 770, 842, 47, 47, 842, 842, 648, 2557, 173, 689, 2291, 1446, 2085, 2557, 2557, 2291, 1780, 1535, 2291, 2391, 808, 691, 1295, 1165, 983, 948, 2000, 948, 983, 983, 2225, 2000, 983, 983, 705, 948, 2000, 1795, 1592, 478, 592, 1795, 1795, 663, 478, 1790, 478, 592, 1592, 173, 901, 312, 4, 1606, 173, 838, 754, 754, 128, 550, 1166, 551, 1480, 550, 550, 1875, 1957, 1166, 902, 1875, 550, 550, 551, 2632, 551, 1875, 1875, 551, 2891, 2159, 2632, 3231, 551, 815, 150, 1654, 1059, 1059, 734, 770, 555, 1592, 555, 2059, 770, 770, 1803, 627, 627, 627, 2059, 931, 1272, 427, 1606, 1272, 1606, 1187, 1204, 397, 822, 21, 1645, 263, 263, 822, 263, 1645, 280, 263, 605, 1645, 2014, 21, 21, 1029, 263, 1916, 2291, 397, 397, 496, 270, 270, 1319, 264, 1638, 264, 986, 1278, 1397, 1278, 1191, 409, 1191, 740, 1191, 754, 754, 387, 63, 948, 666, 666, 1198, 548, 63, 1248, 285, 1248, 169, 1248, 1248, 285, 918, 224, 285, 1426, 1671, 514, 514, 717, 514, 51, 1521, 1745, 51, 605, 1191, 51, 128, 1191, 51, 51, 1521, 267, 513, 952, 966, 1671, 897, 51, 71, 592, 986, 986, 1121, 592, 280, 2000, 2000, 1165, 1165, 1165, 1818, 222, 1818, 1165, 1252, 506, 327, 443, 432, 1291, 1291, 2755, 1413, 520, 1318, 227, 1047, 828, 520, 347, 1364, 136, 136, 452, 457, 457, 132, 457, 488, 1087, 1013, 2225, 32, 1571, 2009, 483, 67, 483,
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Luby, et al. Standards Track [Page 40] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[40ページ]。
740, 740, 1013, 2854, 866, 32, 2861, 866, 887, 32, 2444, 740, 32, 32, 866, 2225, 866, 32, 1571, 2627, 32, 850, 1675, 569, 1158, 32, 1158, 1797, 2641, 1565, 1158, 569, 1797, 1158, 1797, 55, 1703, 42, 55, 2562, 675, 1703, 42, 55, 749, 488, 488, 347, 1206, 1286, 1286, 488, 488, 1206, 1286, 1206, 1286, 550, 550, 1790, 860, 550, 2452, 550, 550, 2765, 1089, 1633, 797, 2244, 1313, 194, 2129, 194, 194, 194, 818, 32, 194, 450, 1313, 2387, 194, 1227, 2387, 308, 2232, 526, 476, 278, 830, 830, 194, 830, 194, 278, 194, 714, 476, 830, 714, 830, 278, 830, 2532, 1218, 1759, 1446, 960, 1747, 187, 1446, 1759, 960, 105, 1446, 1446, 1271, 1446, 960, 960, 1218, 1446, 1446, 105, 1446, 960, 488, 1446, 427, 534, 842, 1969, 2460, 1969, 842, 842, 1969, 427, 941, 2160, 427, 230, 938, 2075, 1675, 1675, 895, 1675, 34, 129, 1811, 239, 749, 1957, 2271, 749, 1908, 129, 239, 239, 129, 129, 2271, 2426, 1355, 1756, 194, 1583, 194, 194, 1583, 194, 1355, 194, 1628, 2221, 1269, 2425, 1756, 1355, 1355, 1583, 1033, 427, 582, 30, 582, 582, 935, 1444, 1962, 915, 733, 915, 938, 1962, 767, 353, 1630, 1962, 1962, 563, 733, 563, 733, 353, 822, 1630, 740, 2076, 2076, 2076, 589, 589, 2636, 866, 589, 947, 1528, 125, 273, 1058, 1058, 1161, 1635, 1355, 1161, 1161, 1355, 1355, 650, 1206, 1206, 784, 784, 784, 784, 784, 412, 461, 412, 2240, 412, 679, 891, 461, 679, 679, 189, 189, 1933, 1651, 2515, 189, 1386, 538, 1386, 1386, 1187, 1386, 2423, 2601, 2285, 175, 175, 2331, 194, 3079, 384, 538, 2365, 2294, 538, 2166, 1841, 3326, 1256, 3923, 976, 85, 550, 550, 1295, 863, 863, 550, 1249, 550, 1759, 146, 1069, 920, 2633, 885, 885, 1514, 1489, 166, 1514, 2041, 885, 2456, 885, 2041, 1081, 1948, 362, 550, 94, 324, 2308, 94, 2386, 94, 550, 874, 1329, 1759, 2280, 1487, 493, 493, 2099, 2599, 1431, 1086, 1514, 1086, 2099, 1858, 368, 1330, 2599, 1858, 2846, 2846, 2907, 2846, 713, 713, 1854, 1123, 713, 713, 3010, 1123, 3010, 538, 713, 1123, 447, 822, 555, 2011, 493, 508, 2292, 555, 1736, 2135, 2704, 555, 2814, 555, 2000, 555, 555, 822, 914, 327, 679, 327, 648, 537, 2263, 931, 1496, 537, 1296, 1745, 1592, 1658, 1795, 650, 1592, 1745, 1745, 1658, 1592, 1745, 1592, 1745, 1658, 1338, 2124, 1592, 1745, 1745, 1745, 837, 1726, 2897, 1118, 1118, 230, 1118, 1118, 1118, 1388, 1748, 514, 128, 1165, 931, 514, 2974, 2041, 2387, 2041, 979, 185, 36, 1269, 550, 173, 812, 36, 1165, 2676, 2562, 1473, 2885, 1982, 1578, 1578, 383, 383, 2360, 383, 1578, 2360, 1584, 1982, 1578, 1578, 1578, 2019, 1036, 355, 724, 2023, 205, 303, 355, 1036, 1966, 355, 1036, 401, 401, 401, 830, 401, 849, 578, 401, 849, 849, 578, 1776, 1123, 552, 2632, 808, 1446, 1120, 373, 1529, 1483, 1057, 893, 1284, 1430, 1529, 1529, 2632, 1352, 2063, 1606, 1352, 1606, 2291, 3079, 2291, 1529, 506, 838, 1606, 1606, 1352, 1529, 1529, 1483, 1529, 1606, 1529, 259, 902, 259, 902, 612, 612, 284, 398, 2991, 1534, 1118, 1118, 1118, 1118, 1118, 734, 284, 2224, 398, 734, 284, 734, 398, 3031, 398, 734, 1707, 2643, 1344, 1477, 475, 1818, 194, 1894, 691, 1528, 1184, 1207, 1501, 6, 2069, 871, 2069, 3548, 1443, 2069, 2685, 3265, 1350, 3265, 2069, 2069, 128, 1313, 128, 663, 414, 1313, 414, 2000, 128, 2000, 663, 1313, 699, 1797, 550, 327, 550, 1526, 699, 327, 1797, 1526, 550, 550, 327, 550, 1426, 1426, 1426, 2285, 1123, 890, 728,
740, 740, 1013, 2854, 866, 32, 2861, 866, 887, 32, 2444, 740, 32, 32, 866, 2225, 866, 32, 1571, 2627, 32, 850, 1675, 569, 1158, 32, 1158, 1797, 2641, 1565, 1158, 569, 1797, 1158, 1797, 55, 1703, 42, 55, 2562, 675, 1703, 42, 55, 749, 488, 488, 347, 1206, 1286, 1286, 488, 488, 1206, 1286, 1206, 1286, 550, 550, 1790, 860, 550, 2452, 550, 550, 2765, 1089, 1633, 797, 2244, 1313, 194, 2129, 194, 194, 194, 818, 32, 194, 450, 1313, 2387, 194, 1227, 2387, 308, 2232, 526, 476, 278, 830, 830, 194, 830, 194, 278, 194, 714, 476, 830, 714, 830, 278, 830, 2532, 1218, 1759, 1446, 960, 1747, 187, 1446, 1759, 960, 105, 1446, 1446, 1271, 1446, 960, 960, 1218, 1446, 1446, 105, 1446, 960, 488, 1446, 427, 534, 842, 1969, 2460, 1969, 842, 842, 1969, 427, 941, 2160, 427, 230, 938, 2075, 1675, 1675, 895, 1675, 34, 129, 1811, 239, 749, 1957, 2271, 749, 1908, 129, 239, 239, 129, 129, 2271, 2426, 1355, 1756, 194, 1583, 194, 194, 1583, 194, 1355, 194, 1628, 2221, 1269, 2425, 1756, 1355, 1355, 1583, 1033, 427, 582, 30, 582, 582, 935, 1444, 1962, 915, 733, 915, 938, 1962, 767, 353, 1630, 1962, 1962, 563, 733, 563, 733, 353, 822, 1630, 740, 2076, 2076, 2076, 589, 589, 2636, 866, 589, 947, 1528, 125, 273, 1058, 1058, 1161, 1635, 1355, 1161, 1161, 1355, 1355, 650, 1206, 1206, 784, 784, 784, 784, 784, 412, 461, 412, 2240, 412, 679, 891, 461, 679, 679, 189, 189, 1933, 1651, 2515, 189, 1386, 538, 1386, 1386, 1187, 1386, 2423, 2601, 2285, 175, 175, 2331, 194, 3079, 384, 538, 2365, 2294, 538, 2166, 1841, 3326, 1256, 3923, 976, 85, 550, 550, 1295, 863, 863, 550, 1249, 550, 1759, 146, 1069, 920, 2633, 885, 885, 1514, 1489, 166, 1514, 2041, 885, 2456, 885, 2041, 1081, 1948, 362, 550, 94, 324, 2308, 94, 2386, 94, 550, 874, 1329, 1759, 2280, 1487, 493, 493, 2099, 2599, 1431, 1086, 1514, 1086, 2099, 1858, 368, 1330, 2599, 1858, 2846, 2846, 2907, 2846, 713, 713, 1854, 1123, 713, 713, 3010, 1123, 3010, 538, 713, 1123, 447, 822, 555, 2011, 493, 508, 2292, 555, 1736, 2135, 2704, 555, 2814, 555, 2000, 555, 555, 822, 914, 327, 679, 327, 648, 537, 2263, 931, 1496, 537, 1296, 1745, 1592, 1658, 1795, 650, 1592, 1745, 1745, 1658, 1592, 1745, 1592, 1745, 1658, 1338, 2124, 1592, 1745, 1745, 1745, 837, 1726, 2897, 1118, 1118, 230, 1118, 1118, 1118, 1388, 1748, 514, 128, 1165, 931, 514, 2974, 2041, 2387, 2041, 979, 185, 36, 1269, 550, 173, 812, 36, 1165, 2676, 2562, 1473, 2885, 1982, 1578, 1578, 383, 383, 2360, 383, 1578, 2360, 1584, 1982, 1578, 1578, 1578, 2019, 1036, 355, 724, 2023, 205, 303, 355, 1036, 1966, 355, 1036, 401, 401, 401, 830, 401, 849, 578, 401, 849, 849, 578, 1776, 1123, 552, 2632, 808, 1446, 1120, 373, 1529, 1483, 1057, 893, 1284, 1430, 1529, 1529, 2632, 1352, 2063, 1606, 1352, 1606, 2291, 3079, 2291, 1529, 506, 838, 1606, 1606, 1352, 1529, 1529, 1483, 1529, 1606, 1529, 259, 902, 259, 902, 612, 612, 284, 398, 2991, 1534, 1118, 1118, 1118, 1118, 1118, 734, 284, 2224, 398, 734, 284, 734, 398, 3031, 398, 734, 1707, 2643, 1344, 1477, 475, 1818, 194, 1894, 691, 1528, 1184, 1207, 1501, 6, 2069, 871, 2069, 3548, 1443, 2069, 2685, 3265, 1350, 3265, 2069, 2069, 128, 1313, 128, 663, 414, 1313, 414, 2000, 128, 2000, 663, 1313, 699, 1797, 550, 327, 550, 1526, 699, 327, 1797, 1526, 550, 550, 327, 550, 1426, 1426, 1426, 2285, 1123, 890, 728,
Luby, et al. Standards Track [Page 41] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[41ページ]。
1707, 728, 728, 327, 253, 1187, 1281, 1364, 1571, 2170, 755, 3232, 925, 1496, 2170, 2170, 1125, 443, 902, 902, 925, 755, 2078, 2457, 902, 2059, 2170, 1643, 1129, 902, 902, 1643, 1129, 606, 36, 103, 338, 338, 1089, 338, 338, 338, 1089, 338, 36, 340, 1206, 1176, 2041, 833, 1854, 1916, 1916, 1501, 2132, 1736, 3065, 367, 1934, 833, 833, 833, 2041, 3017, 2147, 818, 1397, 828, 2147, 398, 828, 818, 1158, 818, 689, 327, 36, 1745, 2132, 582, 1475, 189, 582, 2132, 1191, 582, 2132, 1176, 1176, 516, 2610, 2230, 2230, 64, 1501, 537, 1501, 173, 2230, 2988, 1501, 2694, 2694, 537, 537, 173, 173, 1501, 537, 64, 173, 173, 64, 2230, 537, 2230, 537, 2230, 2230, 2069, 3142, 1645, 689, 1165, 1165, 1963, 514, 488, 1963, 1145, 235, 1145, 1078, 1145, 231, 2405, 552, 21, 57, 57, 57, 1297, 1455, 1988, 2310, 1885, 2854, 2014, 734, 1705, 734, 2854, 734, 677, 1988, 1660, 734, 677, 734, 677, 677, 734, 2854, 1355, 677, 1397, 2947, 2386, 1698, 128, 1698, 3028, 2386, 2437, 2947, 2386, 2643, 2386, 2804, 1188, 335, 746, 1187, 1187, 861, 2519, 1917, 2842, 1917, 675, 1308, 234, 1917, 314, 314, 2339, 2339, 2592, 2576, 902, 916, 2339, 916, 2339, 916, 2339, 916, 1089, 1089, 2644, 1221, 1221, 2446, 308, 308, 2225, 2225, 3192, 2225, 555, 1592, 1592, 555, 893, 555, 550, 770, 3622, 2291, 2291, 3419, 465, 250, 2842, 2291, 2291, 2291, 935, 160, 1271, 308, 325, 935, 1799, 1799, 1891, 2227, 1799, 1598, 112, 1415, 1840, 2014, 1822, 2014, 677, 1822, 1415, 1415, 1822, 2014, 2386, 2159, 1822, 1415, 1822, 179, 1976, 1033, 179, 1840, 2014, 1415, 1970, 1970, 1501, 563, 563, 563, 462, 563, 1970, 1158, 563, 563, 1541, 1238, 383, 235, 1158, 383, 1278, 383, 1898, 2938, 21, 2938, 1313, 2201, 2059, 423, 2059, 1313, 872, 1313, 2044, 89, 173, 3327, 1660, 2044, 1623, 173, 1114, 1114, 1592, 1868, 1651, 1811, 383, 3469, 1811, 1651, 869, 383, 383, 1651, 1651, 3223, 2166, 3469, 767, 383, 1811, 767, 2323, 3355, 1457, 3341, 2640, 2976, 2323, 3341, 2323, 2640, 103, 103, 1161, 1080, 2429, 370, 2018, 2854, 2429, 2166, 2429, 2094, 2207, 871, 1963, 1963, 2023, 2023, 2336, 663, 2893, 1580, 691, 663, 705, 2046, 2599, 409, 2295, 1118, 2494, 1118, 1950, 549, 2494, 2453, 2046, 2494, 2453, 2046, 2453, 2046, 409, 1118, 4952, 2291, 2225, 1894, 1423, 2498, 567, 4129, 1475, 1501, 795, 463, 2084, 828, 828, 232, 828, 232, 232, 1818, 1818, 666, 463, 232, 220, 220, 2162, 2162, 833, 4336, 913, 35, 913, 21, 2927, 886, 3037, 383, 886, 876, 1747, 383, 916, 916, 916, 2927, 916, 1747, 837, 1894, 717, 423, 481, 1894, 1059, 2262, 3206, 4700, 1059, 3304, 2262, 871, 1831, 871, 3304, 1059, 1158, 1934, 1158, 756, 1511, 41, 978, 1934, 2603, 720, 41, 756, 41, 325, 2611, 1158, 173, 1123, 1934, 1934, 1511, 2045, 2045, 2045, 1423, 3206, 3691, 2512, 3206, 2512, 2000, 1811, 2504, 2504, 2611, 2437, 2437, 2437, 1455, 893, 150, 2665, 1966, 605, 398, 2331, 1177, 516, 1962, 4241, 94, 1252, 760, 1292, 1962, 1373, 2000, 1990, 3684, 42, 1868, 3779, 1811, 1811, 2041, 3010, 5436, 1780, 2041, 1868, 1811, 1780, 1811, 1868, 1811, 2041, 1868, 1811, 5627, 4274, 1811, 1868, 4602, 1811, 1811, 1474, 2665, 235, 1474, 2665
1707, 728, 728, 327, 253, 1187, 1281, 1364, 1571, 2170, 755, 3232, 925, 1496, 2170, 2170, 1125, 443, 902, 902, 925, 755, 2078, 2457, 902, 2059, 2170, 1643, 1129, 902, 902, 1643, 1129, 606, 36, 103, 338, 338, 1089, 338, 338, 338, 1089, 338, 36, 340, 1206, 1176, 2041, 833, 1854, 1916, 1916, 1501, 2132, 1736, 3065, 367, 1934, 833, 833, 833, 2041, 3017, 2147, 818, 1397, 828, 2147, 398, 828, 818, 1158, 818, 689, 327, 36, 1745, 2132, 582, 1475, 189, 582, 2132, 1191, 582, 2132, 1176, 1176, 516, 2610, 2230, 2230, 64, 1501, 537, 1501, 173, 2230, 2988, 1501, 2694, 2694, 537, 537, 173, 173, 1501, 537, 64, 173, 173, 64, 2230, 537, 2230, 537, 2230, 2230, 2069, 3142, 1645, 689, 1165, 1165, 1963, 514, 488, 1963, 1145, 235, 1145, 1078, 1145, 231, 2405, 552, 21, 57, 57, 57, 1297, 1455, 1988, 2310, 1885, 2854, 2014, 734, 1705, 734, 2854, 734, 677, 1988, 1660, 734, 677, 734, 677, 677, 734, 2854, 1355, 677, 1397, 2947, 2386, 1698, 128, 1698, 3028, 2386, 2437, 2947, 2386, 2643, 2386, 2804, 1188, 335, 746, 1187, 1187, 861, 2519, 1917, 2842, 1917, 675, 1308, 234, 1917, 314, 314, 2339, 2339, 2592, 2576, 902, 916, 2339, 916, 2339, 916, 2339, 916, 1089, 1089, 2644, 1221, 1221, 2446, 308, 308, 2225, 2225, 3192, 2225, 555, 1592, 1592, 555, 893, 555, 550, 770, 3622, 2291, 2291, 3419, 465, 250, 2842, 2291, 2291, 2291, 935, 160, 1271, 308, 325, 935, 1799, 1799, 1891, 2227, 1799, 1598, 112, 1415, 1840, 2014, 1822, 2014, 677, 1822, 1415, 1415, 1822, 2014, 2386, 2159, 1822, 1415, 1822, 179, 1976, 1033, 179, 1840, 2014, 1415, 1970, 1970, 1501, 563, 563, 563, 462, 563, 1970, 1158, 563, 563, 1541, 1238, 383, 235, 1158, 383, 1278, 383, 1898, 2938, 21, 2938, 1313, 2201, 2059, 423, 2059, 1313, 872, 1313, 2044, 89, 173, 3327, 1660, 2044, 1623, 173, 1114, 1114, 1592, 1868, 1651, 1811, 383, 3469, 1811, 1651, 869, 383, 383, 1651, 1651, 3223, 2166, 3469, 767, 383, 1811, 767, 2323, 3355, 1457, 3341, 2640, 2976, 2323, 3341, 2323, 2640, 103, 103, 1161, 1080, 2429, 370, 2018, 2854, 2429, 2166, 2429, 2094, 2207, 871, 1963, 1963, 2023, 2023, 2336, 663, 2893, 1580, 691, 663, 705, 2046, 2599, 409, 2295, 1118, 2494, 1118, 1950, 549, 2494, 2453, 2046, 2494, 2453, 2046, 2453, 2046, 409, 1118, 4952, 2291, 2225, 1894, 1423, 2498, 567, 4129, 1475, 1501, 795, 463, 2084, 828, 828, 232, 828, 232, 232, 1818, 1818, 666, 463, 232, 220, 220, 2162, 2162, 833, 4336, 913, 35, 913, 21, 2927, 886, 3037, 383, 886, 876, 1747, 383, 916, 916, 916, 2927, 916, 1747, 837, 1894, 717, 423, 481, 1894, 1059, 2262, 3206, 4700, 1059, 3304, 2262, 871, 1831, 871, 3304, 1059, 1158, 1934, 1158, 756, 1511, 41, 978, 1934, 2603, 720, 41, 756, 41, 325, 2611, 1158, 173, 1123, 1934, 1934, 1511, 2045, 2045, 2045, 1423, 3206, 3691, 2512, 3206, 2512, 2000, 1811, 2504, 2504, 2611, 2437, 2437, 2437, 1455, 893, 150, 2665, 1966, 605, 398, 2331, 1177, 516, 1962, 4241, 94, 1252, 760, 1292, 1962, 1373, 2000, 1990, 3684, 42, 1868, 3779, 1811, 1811, 2041, 3010, 5436, 1780, 2041, 1868, 1811, 1780, 1811, 1868, 1811, 2041, 1868, 1811, 5627, 4274, 1811, 1868, 4602, 1811, 1811, 1474, 2665, 235, 1474, 2665
Luby, et al. Standards Track [Page 42] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[42ページ]。
6. Security Considerations
6. セキュリティ問題
Data delivery can be subject to denial-of-service attacks by attackers that send corrupted packets that are accepted as legitimate by receivers. This is particularly a concern for multicast delivery because a corrupted packet may be injected into the session close to the root of the multicast tree, in which case, the corrupted packet will arrive at many receivers. This is particularly a concern when the code described in this document is used because the use of even one corrupted packet containing encoding data may result in the decoding of an object that is completely corrupted and unusable. It is thus RECOMMENDED that source authentication and integrity checking are applied to decoded objects before delivering objects to an application. For example, a SHA-1 hash [SHA1] of an object may be appended before transmission, and the SHA-1 hash is computed and checked after the object is decoded but before it is delivered to an application. Source authentication SHOULD be provided, for example, by including a digital signature verifiable by the receiver computed on top of the hash value. It is also RECOMMENDED that a packet authentication protocol, such as TESLA [RFC4082], be used to detect and discard corrupted packets upon arrival. This method may also be used to provide source authentication. Furthermore, it is RECOMMENDED that Reverse Path Forwarding checks be enabled in all network routers and switches along the path from the sender to receivers to limit the possibility of a bad agent successfully injecting a corrupted packet into the multicast tree data path.
データ配送は受信機で正統であるとして認められる崩壊したパケットを送る攻撃者によるサービス不能攻撃を受けることがある場合があります。 これが崩壊したパケットがマルチキャスト木の根の近くでのセッションに注がれるかもしれないので特にマルチキャスト配送に関する心配である、その場合、崩壊したパケットは多くの受信機に到着するでしょう。 データを暗号化を含む1つの崩壊したパケットさえの使用が完全に崩壊して使用不可能な物の解読をもたらすかもしれないので本書では説明されたコードが使用されているとき、これは特に関心です。 その結果、物をアプリケーションに届ける前にソース認証と保全の照合が解読された物に適用されるのは、RECOMMENDEDです。 例えば、トランスミッションの前に物のSHA-1細切れ肉料理[SHA1]を追加するかもしれなくて、物を解読した後にもかかわらず、それをアプリケーションに届ける前を除いて、SHA-1細切れ肉料理は、計算されて、チェックされます。 ソース認証SHOULDを提供して、例えば、包含することによって、受信機で証明可能なデジタル署名はハッシュ値の上で計算されました。 また、パケット認証プロトコルが到着のときに崩壊したパケットを検出して、捨てるのにテスラ[RFC4082]などのように使用されるのは、RECOMMENDEDです。 また、この方法は、認証をソースに提供するのに使用されるかもしれません。 その上、Reverse Path ForwardingがチェックするRECOMMENDEDが首尾よく悪いエージェントの可能性を制限するためにマルチキャスト木のデータ経路に崩壊したパケットを注ぎながらすべてのネットワークルータで可能にされて、経路に沿って送付者から受信機に切り替わるということです。
Another security concern is that some FEC information may be obtained by receivers out-of-band in a session description, and if the session description is forged or corrupted, then the receivers will not use the correct protocol for decoding content from received packets. To avoid these problems, it is RECOMMENDED that measures be taken to prevent receivers from accepting incorrect session descriptions, e.g., by using source authentication to ensure that receivers only accept legitimate session descriptions from authorized senders.
別のセキュリティ関心はバンドの外で受信機でセッション記述で何らかのFEC情報を得るかもしれないということであり、セッション記述が鍛造されるか、または崩壊すると、受信機は、容認されたパケットから内容を解読するのに正しいプロトコルを使用しないでしょう。 対策が受信機が不正確なセッション記述を受け入れるのを防ぐために実施されるのは、これらの問題を避けるためには、RECOMMENDEDです、例えば、受信機が認可された送付者から正統のセッション記述を受け入れるだけであるのを保証するのにソース認証を使用することによって。
7. IANA Considerations
7. IANA問題
Values of FEC Encoding IDs and FEC Instance IDs are subject to IANA registration. For general guidelines on IANA considerations as they apply to this document, see [RFC5052]. This document assigns the Fully-Specified FEC Encoding ID 1 under the ietf:rmt:fec:encoding name-space to "Raptor Code".
FEC Encoding IDとFEC Instance IDの値はIANA登録を受けることがあります。 IANA問題に関する一般的ガイドラインに関しては、それらがこのドキュメントに適用するとき、[RFC5052]を見てください。 このドキュメントはietf: rmt: fecの下でFullyによって指定されたFEC Encoding ID1を割り当てます: 「猛きん類コード」に名前スペースをコード化します。
Luby, et al. Standards Track [Page 43] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[43ページ]。
8. Acknowledgements
8. 承認
Numerous editorial improvements and clarifications were made to this specification during the review process within 3GPP. Thanks are due to the members of 3GPP Technical Specification Group SA, Working Group 4, for these.
吟味の過程の間、3GPPの中で頻繁な編集の改良と明確化をこの仕様にしました。 感謝は3GPP仕様書Group SAのこれらのための作業部会4のメンバーのためです。
9. References
9. 参照
9.1. Normative References
9.1. 引用規格
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2119] ブラドナー、S.、「Indicate Requirement LevelsへのRFCsにおける使用のためのキーワード」、BCP14、RFC2119、1997年3月。
[RFC4082] Perrig, A., Song, D., Canetti, R., Tygar, J., and B.
Briscoe, "Timed Efficient Stream Loss-Tolerant
Authentication (TESLA): Multicast Source Authentication
Transform Introduction", RFC 4082, June 2005.
[RFC4082] Perrig、A.、歌、D.、カネッティ、R.、Tygar、J.、およびB.ブリスコウ、「効率的な状態で調節されて、損失許容性がある認証(テスラ)を流してください」 「マルチキャストソース認証変換序論」、RFC4082、2005年6月。
[RFC5052] Watson, M., Luby, M., and L. Vicisano, "Forward Error
Correction (FEC) Building Block", RFC 5052, August 2007.
[RFC5052] ワトソンとM.とLuby、M.とL.Vicisano、「前進型誤信号訂正(FEC)ブロック」、RFC5052、2007年8月。
9.2. Informative References
9.2. 有益な参照
[CCNC] Luby, M., Watson, M., Gasiba, T., Stockhammer, T., and W.
Xu, "Raptor Codes for Reliable Download Delivery in
Wireless Broadcast Systems", CCNC 2006, Las Vegas, NV ,
Jan 2006.
[CCNC] Luby、M.、ワトソン、M.、Gasiba、T.、Stockhammer、T.、およびW.シュー、「無線の放送システムにおける信頼できるダウンロード配送のための猛きん類コード」、CCNC2006、ラスベガス(ネバダ)2006年1月。
[MBMS] 3GPP, "Multimedia Broadcast/Multicast Service (MBMS);
Protocols and codecs", 3GPP TS 26.346 6.1.0, June 2005.
[MBMS]3GPP、「マルチメディア放送/マルチキャストサービス(MBMS)」。 3GPP TS26.346 6.1の「プロトコルとコーデック」、.0、6月2005日
[RFC3453] Luby, M., Vicisano, L., Gemmell, J., Rizzo, L., Handley,
M., and J. Crowcroft, "The Use of Forward Error Correction
(FEC) in Reliable Multicast", RFC 3453, December 2002.
[RFC3453] Luby、M.、Vicisano、L.、Gemmell、J.、リゾー、L.、ハンドレー、M.、およびJ.クロウクロフト、「信頼できるマルチキャストにおける前進型誤信号訂正(FEC)の使用」、RFC3453(2002年12月)。
[Raptor] Shokrollahi, A., "Raptor Codes", IEEE Transactions on
Information Theory no. 6, June 2006.
[猛きん類] Shokrollahi、A.、「猛きん類コード」、情報Theory No.6のIEEE Transactions、2006年6月。
[SHA1] "Secure Hash Standard", Federal Information Processing
Standards Publication (FIPS PUB) 180-1, April 2005.
[SHA1]「安全な細切れ肉料理規格」、連邦政府の情報処理規格公表(FIPSパブ)180-1、2005年4月。
Luby, et al. Standards Track [Page 44] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[44ページ]。
Authors' Addresses
作者のアドレス
Michael Luby Digital Fountain 39141 Civic Center Drive Suite 300 Fremont, CA 94538 U.S.A.
フレモント、マイケルLubyのデジタル噴水39141シビック・センタードライブスイート300カリフォルニア94538米国
EMail: luby@digitalfountain.com
メール: luby@digitalfountain.com
Amin Shokrollahi EPFL Laboratory of Algorithmic Mathematics IC-IIF-ALGO PSE-A Lausanne 1015 Switzerland
アミン・Shokrollahi EPFLアルゴリズムの数学IC IIF痛PSE-Aローザンヌ研究所1015スイス
EMail: amin.shokrollahi@epfl.ch
メール: amin.shokrollahi@epfl.ch
Mark Watson Digital Fountain 39141 Civic Center Drive Suite 300 Fremont, CA 94538 U.S.A.
フレモント、マークワトソンデジタル噴水39141シビック・センタードライブスイート300カリフォルニア94538米国
EMail: mark@digitalfountain.com
メール: mark@digitalfountain.com
Thomas Stockhammer Nomor Research Brecherspitzstrasse 8 Munich 81541 Germany
トーマスStockhammer Nomor研究Brecherspitzstrasse8ミュンヘン81541ドイツ
EMail: stockhammer@nomor.de
メール: stockhammer@nomor.de
Luby, et al. Standards Track [Page 45] RFC 5053 Raptor FEC Scheme October 2007
Luby、他 規格は猛きん類FEC計画2007年10月にRFC5053を追跡します[45ページ]。
Full Copyright Statement
完全な著作権宣言文
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IETFが信じる著作権(C)(2007)。
This document is subject to the rights, licenses and restrictions contained in BCP 78, and except as set forth therein, the authors retain all their rights.
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知的所有権
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Luby, et al. Standards Track [Page 46]
Luby、他 標準化過程[46ページ]
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