US9270414B2 - Multiple-field based code generator and decoder for communications systems - Google Patents
Multiple-field based code generator and decoder for communications systems Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0041—Arrangements at the transmitter end
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/37—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35
- H03M13/3761—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35 using code combining, i.e. using combining of codeword portions which may have been transmitted separately, e.g. Digital Fountain codes, Raptor codes or Luby Transform [LT] codes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0045—Arrangements at the receiver end
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0057—Block codes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0064—Concatenated codes
- H04L1/0065—Serial concatenated codes
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/13—Linear codes
- H03M13/19—Single error correction without using particular properties of the cyclic codes, e.g. Hamming codes, extended or generalised Hamming codes
Abstract
Description
00 | 01 | 10 | 11 | ||
00 | 00 | 00 | 00 | 00 |
01 | 00 | 10 | 10 | 11 |
10 | 00 | 10 | 11 | 10 |
11 | 00 | 11 | 10 | 10 |
00*S=0
01*S=S
10*S=(S[1], S[0]⊕S[1])
11*S=(S[0]⊕S[1],S[0]).
00*S=0
01*S=S
10*S=(S[1]|S[0]⊕S[1])
11*S=(S[0]⊕S[1]|S[0]).
X=B{circle around (×)}S.
for all j from 1 to m, X j =B[j,1]*S 1 ⊕B[j,2]*S 2 ⊕ . . . ⊕B[j,n]*S n
-
- wherein “*” denotes either a simple or an interleaved transformation.
- Source block: a block of K source symbols which are considered together for MSCR encoding purposes.
- Source symbol: the smallest unit of data used during the encoding process. All source symbols within a source block have the same size.
- Encoding symbol: a symbol that is included in a data packet. The encoding symbols comprise 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.
- Systematic code: a code in which the source symbols are included as part of the encoding symbols sent for a source block.
- 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.
- 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.
- Symbol: a unit of data. The size, in bytes, of a symbol is known as the symbol size.
- 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.
- Encoding Symbol ID: information that defines the relationship between the symbols of an encoding symbol group and the source symbols.
- Encoding packet: data packets that contain encoding symbols
- Sub-block: a source block is sometime broken into sub-blocks, each of which is sufficiently small to be decoded in working memory. For a source block comprising K source symbols, each sub-block comprises K sub-symbols, each symbol of the source block being composed of one sub-symbol from each sub-block.
- 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.
- Source packet: data packets that contain source symbols. Repair packet: data packets that contain repair symbols.
B.1.2. Symbols
i, j, x, h, a, b, d, | represent positive integers |
v, m | |
ceil(x) | denotes the smallest positive integer which is greater than or equal to x |
choose(i, j) | denotes the number of ways j objects can be chosen from among i objects |
without repetition | |
floor(x) | denotes the largest positive integer which is less than or equal to x |
i % j | denotes i modulo j |
X {circumflex over ( )} Y | denotes, for equal-length bit strings X and Y, the bitwise exclusive-or of X and |
Y | |
A | denote a symbol alignment parameter. Symbol and sub-symbol sizes are |
restricted to be multiples of A. | |
AT | denotes the transposed matrix of matrix A |
A−1 | denotes the inverse matrix of matrix A |
K | denotes the number of symbols in a single source block |
KMAX | denotes the maximum number of source symbols that can be in a single source |
block. Set to 8192. Note that other values might be used. | |
L | denotes the number of pre-coding symbols for a single source block |
S | denotes the number of LDPC symbols for a single source block |
H | denotes the number of Half symbols for a single source block |
C | denotes an array of intermediate symbols, C[0], C[1], C[2], . . . , C[L − 1] |
C′ | denotes an array of source symbols, C′[0], C′[1], C′[2], . . . , C′[K − 1] |
X | a non-negative integer value |
V0, V1 | two arrays of 4-byte integers, V0[0], V0[1], . . . , V0[255]; V1[0], V1[1], . . . , V1[255] |
Rand[X, i, m] | a pseudo-random number generator |
Deg[ν] | a degree generator |
LTEnc[K, C, (d, | a LT encoding symbol generator |
a, b)] | |
Trip[K, X] | a triple generator function |
G | the number of symbols within an encoding symbol group |
N | the number of sub-blocks within a source block |
T | the symbol size in bytes. If the source block is partitioned into sub-blocks, |
then T = T′ · N. | |
T′ | the sub-symbol size, in bytes. If the source block is not partitioned into sub- |
blocks then T′ is not relevant. | |
F | the file size, for file download, in bytes |
I | the sub-block size in bytes |
P | for file download, the payload size of each packet, in bytes, that is used in one |
preferred derivation of the file download transport parameters. For streaming, | |
the payload size of each repair packet, in bytes, that is used in one preferred | |
derivation of the streaming transport parameters. | |
Q | Q = 65521, i.e., Q is the largest prime smaller than 216. Note that other values |
might be used instead of 216. | |
Z | the number of source blocks, for file download |
J(K) | the systematic index associated with K |
G | denotes any generator matrix |
IS | denotes the S × |
0S×H | denotes the S × H zero matrix |
B.1.3 Abbreviations
For the purposes of the present document, the following abbreviations apply:
ESI: | Encoding Symbol ID | ||
LDPC: | Low Density Parity Check | ||
LT: | Luby Transform | ||
SBN: | Source Block Number | ||
SBL: | Source Block Length (in units of symbols) | ||
B.2. Overview
- F the size of the file, in bytes
- A a symbol alignment parameter, in bytes
- T the symbol size, in bytes, which preferably is a multiple of A
- Z the number of source blocks
- N the number of sub-blocks in each source block
- Kt=ceil(F/T)
- (KL, KS, ZL, ZS)=Partition[Kt,Z]
- (TL, TS, NL, NS)=Partition[T/A, N]
- For each i=0, . . . , G−1
- (d[i], a[i], b[i])=Trip[K,X+i]
- F the file size, in bytes
- W a target on the sub-block size, in bytes
- P the maximum packet payload size, in bytes, which is assumed to be a multiple of A
- A the symbol alignment factor, in bytes
- KMAX the maximum number of source symbols per source block.
- KMIN a minimum target on the number of symbols per source block
- GMAX a maximum target number of symbols per packet
G=min{ceil(P·K MIN /F), P/A, G MAX}−the approximate number of symbols per packet
T=floor(P/(A·G))·A
K t=ceil(F/T)−the total number of symbols in the file
Z=ceil(K t /K MAX)
N=min{ceil(ceil(K t /Z)·T/W), T/A}
B | the maximum source block size, in bytes |
Pmax | the maximum Source Packet Information size, without padding |
Pr | the xth percentile Source Packet Information size, without |
padding (i.e. the least number, n, such that x % of the packets | |
are expected to have Source Packet Information size n or less. | |
In one embodiment, the value of x is 30. | |
A | the symbol alignment factor, in bytes |
KMAX | the maximum number of source symbols per source block. |
KMIN | a minimum target on the number of symbols per source block |
GMAX | a maximum target number of symbols per repair packet |
Let G=min{max{ceil(P·K MIN /B), floor(P x /P max)}, P/A, G MAX}−the number of symbols per SPI
T=floor(P/(A·G))·A
- Let C′[0], . . . , C′[K−1] denote the K source symbols.
- Let C′[0], . . . , C′[L−1] denote L intermediate symbols.
-
- 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 B.5.2.2 using the Trip[ ] generator as described in Section B.5.4.4.
- 2. A set of pre-coding relationships hold within the intermediate symbols themselves.
- For each i, 0≦i<K
- (d[i], a[i], b[i])=Trip[K, i]
B.5.2.3 Pre-Coding Relationships
- 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
- H be the smallest integer such that choose(H, ceil(H/2))≧K+S
- H′=ceil(H/2)
- L=K+S+H
- C[0], . . . , C[K−1] denote the first K intermediate symbols
- C[K], . . . , C[K+S−1] denote the S LDPC symbols, initialized to zero
- C[K+S], . . . , C[L−1] denote the HHDPC symbols, initialized to zero
- For i=0, . . . , K−1 do
- a=1+(floor(i/S) % (S−1))
- b=i % S
- C[K+b]=C[K+b]^C[i]
- b=(b+a) % S
- C[K+b]=C[K+b]^C[i]
- b=(b+a) % S
- C[K+b]=C[K+b]^C[i]
-
- 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
- 2. The L intermediate symbols C[0], C[1], . . . , C[L−1] satisfy the pre-coding relationships defined in B.5.2.3.
B.5.2.4.2 Calculation of Intermediate Symbols
- C denote the column vector of the L intermediate symbols, C[0], C[1], . . . , C[L−1].
- D denote the column vector comprising S+H zero symbols followed by the K source symbols C′[0], C′[1], . . . , C′[K−1]
Then the above constraints define an L×L matrix over GF(2), A, such that:
A·C=D
The matrix A can be constructed as follows:
Let: - GLDPC be the S×K generator matrix of the LDPC symbols. So,
- GLDPC (C[0], . . . , C[K−1])T=(C[K], . . . , C[K+S−1])T
- GHDPC be the H×(K+S) generator matrix of the Half symbols, So,
- GHDPC{circle around (×)}(C[0], . . . , C[S+K−1])T=(C[K+S], . . . , C[K+S+H−1])T
- IS be the S×S identity matrix
- IH be the H×H identity matrix
- OS×H be the S×H zero matrix
- GLT be the K×L generator matrix of the encoding symbols generated by the LT Encoder. So,
- GLT·(C[0], . . . , C[L−1])T=(C′[0], C′[1], . . . , C′[K−1])T
- i.e., GLTi,j=1 if and only if C[i] is included in the symbols which are XORed to produce LTEnc[K, (C[0], . . . , C[L−1]), (d[i], a[i], b[i])].
Then: - The first S rows of A are equal to GLDPC|IS|ZS×H.
- The next H rows of A are equal to GHDPC|IH.
- The remaining K rows of A are equal to GLT.
C=A −1 ·D
- Deg[v]=d[j]
B.5.4.3 Chain Reaction Encoding Symbol Generator
- While (b≧L) do b=(b+a) % L′
- LTEnc[K,(C[0], C[1], . . . , C[L−1]), (d, a, b)]=C[b].
- For j=1, . . . , min(d−1,L−1) do
- b=(b+a) % L′
- While (b≧L) do b=(b+a) % L′
- LTEnc[K, (C[0], C[1], . . . , C[L−1]), (d, a, b)]=LTEnc[K, (C[0], C[1], . . . , C[L−1]), (d, a, b)]^C[b]
B.5.4.4 Triple Generator
- K The number of source symbols
- X An encoding symbol ID
Let - L be determined from K as described in Section B.5.2
- L′ be the smallest prime that is greater than or equal to L
- Q=65521, the largest prime smaller than 216.
- J(K) be the systematic index associated with K. The systematic index is a number chosen such that the process below, together which the remaining processed for construction of the matrix A described herein results in a matrix B which is invertible. Suitable systematic indices are provided in Appendix A by way of example only and should not be construed as to limit the scope of the invention.
- 1. A=(53591+J(K)·997) % Q
- 2. B=10267·(J(K)+1) % Q
- 3. Y=(B+X·A) % Q
- 4. v=Rand[Y, 0, 220]
- 5. d=Deg[v]
- 6. a=1+Rand[Y, 1, L′−1]
- 7. b=Rand[Y, 2, L′]
B.6 FEC Decoder Implementations
B.6.1 General
-
- (1) The submatrix 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.
- (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.
- (4) The submatrix U defined by the intersection of all the rows and the last u columns.
- (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.
- If r=1, then choose the row with exactly one 1 in V.
- 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 Y.
- If r>2 then choose a row with exactly r ones in V with minimum original weight among all such rows.
-
- selecting according to a random process an integer greater than zero, d, known as the degree of the output symbol,
- selecting according to a random process, a set of size d of input symbols, this set of input symbols to be known as the neighbor set of the output symbol,
- selecting a set of finite fields, such that for at least one output symbol this set contains at least two finite fields,
- selecting for each input symbol in the neighbor set of the output symbol a finite field from the selected set of possible finite fields,
- selecting for each input symbols in the neighbor set of the output symbol, according to a random process, a non-zero element from the finite field selected above.
Claims (83)
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US11/674,655 US9270414B2 (en) | 2006-02-21 | 2007-02-13 | Multiple-field based code generator and decoder for communications systems |
CN2007800139722A CN101427495B (en) | 2006-02-21 | 2007-02-16 | Multiple-field based code generator and decoder for communications systems |
PCT/US2007/062302 WO2007098397A2 (en) | 2006-02-21 | 2007-02-16 | Multiple-field based code generator and decoder for communications systems |
EP07757111.5A EP1980041B1 (en) | 2006-02-21 | 2007-02-16 | Multiple-field based code generator and decoder for communications systems |
KR1020087022501A KR101355761B1 (en) | 2006-02-21 | 2007-02-16 | Multiple-field based code generator and decoder for communications systems |
ES07757111.5T ES2563290T3 (en) | 2006-02-21 | 2007-02-16 | Multi-field based code generator and decoder for communications systems |
JP2008555514A JP5329239B2 (en) | 2006-02-21 | 2007-02-16 | Multi-body code generator and decoder for communication systems |
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ES2563290T3 (en) | 2016-03-14 |
WO2007098397A2 (en) | 2007-08-30 |
CN101427495A (en) | 2009-05-06 |
KR101355761B1 (en) | 2014-01-24 |
CN101427495B (en) | 2013-12-25 |
KR20080100455A (en) | 2008-11-18 |
JP2009527949A (en) | 2009-07-30 |
EP1980041A2 (en) | 2008-10-15 |
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