CN102055485A - Quasi-cyclic low-density parity-check (QC-LDPC) code and correcting and linear coding method thereof - Google Patents

Quasi-cyclic low-density parity-check (QC-LDPC) code and correcting and linear coding method thereof Download PDF

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CN102055485A
CN102055485A CN2010106058385A CN201010605838A CN102055485A CN 102055485 A CN102055485 A CN 102055485A CN 2010106058385 A CN2010106058385 A CN 2010106058385A CN 201010605838 A CN201010605838 A CN 201010605838A CN 102055485 A CN102055485 A CN 102055485A
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吴晓富
崔龙
赵春明
尤肖虎
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PLA University of Science and Technology
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Abstract

The invention relates to a quasi-cyclic low-density parity-check (QC-LDPC) code and a correcting and linear coding method thereof. The variable nodes of the LDPC code, the dimensionality of which is greater than 2, are informational nodes; and the variable nodes the dimensionality of which is 2 form a big end-to-end ring on a bipartite graph. The correcting method comprises the following implementation steps: randomly selecting one edge on the big ring the dimensionality of which is 2, cutting off the edge, and filling 0 in the corresponding position of a low-density check matrix, thereby acquiring a corrected structure of the code. The linear coding method of the corrected code comprises the following implementation steps: firstly, multiplying an input information vector s and a part of the check matrix the load of which is greater than 2 as a vector by a matrix to acquire an intermediate vector u; directly intercepting the corresponding position of the intermediate vector u to acquire a coding vector the variable node dimensionality of which is 1; computing bit by bit from a start bit according to the characteristics of the big ring on the bipartite graph to acquire a coding vector the variable node dimensionality of which is 2; and combining the two coding vectors to finally form a coding vector.

Description

Quasi-cyclic low-density parity check codes and correction thereof and uniform enconding method
Technical field
The present invention is the coding method of low density parity check code, belongs to the code construction and the coding method field of channel error correction coding.
Background technology
At low-density checksum (Low-Density Parity-Check, abbreviation LDPC) in the middle of the coding method of sign indicating number, Richardson is at document (T.J. Richardson and R.L. Urbanke, " Efficient encoding of low-density parity-check codes; " IEEE Trans. Inform. Theory, vol.47, no.2, pp. 638-656, Feb. 2001.) in coding method based on triangle check matrix under the class has been proposed.If but the verification battle array can't be adjusted to desirable class lower triangular matrix form, then Bian Ma complexity is still very high.From the hard-wired angle of LDPC coder, structureless LDPC sign indicating number is unfavorable for the hardware realization.For this reason, has accurate circulation (Quasi-Cyclic, abbreviation QC) the LDPC sign indicating number of structure has obtained the extensive favor of academia and industrial quarters, the QC structure is reflected on the check matrix of LDPC sign indicating number has following characteristics: check matrix is made up of the cyclic shift submatrix, the cyclic shift submatrix then be unit matrix through the resulting square formation of cyclic shift, so cyclic shift matrices is decided by the coefficient that is shifted fully under the given prerequisite of matrix size.Discover that the QC structure can be simplified the design of encoder, the encoder of a lot of QC-LDPC sign indicating numbers can utilize circulating register effectively to realize.Yet QC designs simplification encoder also exists serious restricting relation: must there be a full rank submatrix that is made of the circulation submatrix in check matrix.In actual configuration, this condition also is not easy to satisfy.
In the low code rate LDPC code structure, for improving performance, generally need to introduce implicit variable node, then be equivalent in the check matrix of LDPC sign indicating number, introduce more row (1 variable node is corresponding to the row of 1 in the check matrix), also be that the corresponding codes bit does not send on the channel, thereby be referred to as to have the LDPC sign indicating number of implicit node, document (T. Richardson and R. Urbanke for example, " Multi-Edge type LDPC Codes; " http://lthcwww.epfl.ch/) polygonal LDPC sign indicating number of Ti Chuing or document (A. Abbasfar, D. Divsalar, and K. Yao, " Accumulate Repeat Accumulate Codes; " in IEEE International Symposium on Information Theory, (Chicago, Illinois), June 2004.) middle adding up-repeat-sign indicating number that adds up (Accumulate-Repeat-Accumulate is called for short ARA) sign indicating number of proposing.
For ease of realizing that the LDPC sign indicating number with implicit node also should adopt accurate loop structure, also is the so-called implicit node quasi-cyclic low-density parity check codes that has.But this accurate loop structure often can not find good coding method, and this is because accurate loop structure makes that the submatrix that finds the message length size that is made of the sub-square of cyclic shift in the check matrix is the possibility of full rank and little.For this reason, the present invention adjusts the structure with implicit node quasi-cyclic low-density parity check codes, and has provided a kind of linear coding method based on this.
Summary of the invention
Technical problem:The correction and the uniform enconding method thereof that the purpose of this invention is to provide a kind of quasi-cyclic low-density parity check codes solve the problem that the linear complexity coding of such low density parity check code is difficult to design.
Technical scheme:The dimension of quasi-cyclic low-density parity check codes variable node of the present invention is divided into 3 classes: dimension is 1, dimension be 2 and dimension greater than 2; Dimension all is an information node greater than 2 variable node, corresponding to information bit to be encoded position, owing to generally do not send on the channel, thereby be referred to as implicit node; Dimension is that 2 variable node just in time forms an end to end big ring on the bipartite graph of corresponding low-density check matrix correspondence.
The modification method of quasi-cyclic low-density parity check codes of the present invention is: be optional limit on 2 the big ring in described dimension, it is clipped, also promptly fill out 0 in the relevant position of low-density check matrix, thereby obtain this a kind of correcting principle of encoding; The row of filling out 0 operation place in the check matrix is called coding and starts row as the position that coding begins to start.
Described correcting principle is embodied in the modification to the check matrix of low density parity check code, retouching operation is 2 row to the column weight that likes the big ring of formation in the check matrix, appoint " 1 " get row wherein it to be set to " 0 ", the row that displacement takes place is called to start goes, and this correcting principle specifically is expressed as in conjunction with the definition of check matrix:
Definition:One class has the check matrix of implicit node quasi-cyclic low-density parity check codes:
Figure 888274DEST_PATH_IMAGE001
Wherein, Be that size is
Figure 550779DEST_PATH_IMAGE003
The cyclic shift permutation submatrix, this matrix depends on the cyclic shift amount fully,
Figure 903263DEST_PATH_IMAGE004
The line number that accounts for for cyclic shift permutation submatrix in the check matrix,
Figure 580232DEST_PATH_IMAGE005
Be the columns that cyclic shift permutation submatrix in the check matrix accounts for, should
Figure 80483DEST_PATH_IMAGE006
The size of matrix is
Figure 766680DEST_PATH_IMAGE007
Be convenient coding, this type of check matrix is divided into 3 parts:
Figure 35987DEST_PATH_IMAGE008
, wherein,
Figure 149436DEST_PATH_IMAGE009
Corresponding to the information bit part of complete code, size is
Figure 136984DEST_PATH_IMAGE010
One-dimensional degree check matrix
Figure 361292DEST_PATH_IMAGE011
Corresponding to code word one-dimensional degree column weight is 1 check bit part, and size is
Figure 688368DEST_PATH_IMAGE012
Two dimension check matrixes
Figure 536501DEST_PATH_IMAGE013
Corresponding to the two dimension column weights of code word is 2 check bit part, and size is
Figure 683448DEST_PATH_IMAGE014
The total length of coding is
Figure 773764DEST_PATH_IMAGE015
Because
Figure 955347DEST_PATH_IMAGE016
Corresponding codes codeword information bit position does not send on the channel, thereby is the loe-density parity-check code with implicit node; Described pair of dimension check matrix
Figure 472916DEST_PATH_IMAGE017
All " 1 " constitutes a big ring, establishes two dimension check matrixes
Figure 372738DEST_PATH_IMAGE017
In " 1 " be followed successively by according to the coordinate of counterclockwise order in this matrix of big ring
Figure 938849DEST_PATH_IMAGE018
Described pair of dimension check matrix
Figure 37255DEST_PATH_IMAGE017
In formulate arbitrarily one of them " 1 ", it is changed to " 0 ", amended pair of dimension check matrix is designated as
Figure 227190DEST_PATH_IMAGE019
, the loe-density parity-check code of final correcting principle has check matrix:
。
The uniform enconding method of quasi-cyclic low-density parity check codes of the present invention is: utilize the low-density check matrix of correcting principle and input information bits vector to calculate bits of coded: at first to utilize the input information vector s, the multiplication mutually of doing vector and matrix greater than 2 part with the column weight of check matrix obtains middle vector uThe variable node dimension is 1 coded vector
Figure 780848DEST_PATH_IMAGE021
Vector in the middle of directly intercepting uThe relevant position obtain; The variable node dimension is 2 coded vector
Figure 937023DEST_PATH_IMAGE022
Then begin to calculate and to get by start bit, two parts coded vector is pieced together final formation coding output vector by bit by its big ring property on bipartite graph
7. the uniform enconding method of quasi-cyclic low-density parity check codes according to claim 6 is characterized in that described coded vector separated into two parts carries out, and a part is 1 row corresponding to the check matrix column weight, gets by the dope vector direct coding; Another part is 2 row corresponding to the check matrix column weight, and the respective coding vector can calculate by bit by big ring property and get, and this encryption algorithm specifically is expressed as the several steps of execution in the following order: Definition:If the input vector of encoder is
Figure 467547DEST_PATH_IMAGE024
, wherein
Figure 375461DEST_PATH_IMAGE025
Encoder is output as coding codeword, is designated as If the corresponding implicit node of information bit, then information bit does not send, and encoder is output as
Figure 980197DEST_PATH_IMAGE027
, wherein, Corresponding to the coded vector of one-dimensional degree check matrix, its size is made as Corresponding to the coded vector of two dimension check matrixes, its size is made as
Figure 745973DEST_PATH_IMAGE031
With matrix
Figure 63821DEST_PATH_IMAGE009
Write as matrix in block form , wherein
Figure 626707DEST_PATH_IMAGE033
Size be
Figure 936465DEST_PATH_IMAGE034
, Size be , and
Figure 759431DEST_PATH_IMAGE037
Step 1:Utilize the input information bits vector
Figure 240091DEST_PATH_IMAGE038
And check matrix
Figure 798111DEST_PATH_IMAGE033
, multiply each other and directly calculate
Figure 941692DEST_PATH_IMAGE039
Step 2:Utilize the input information bits vector And check matrix
Figure 615436DEST_PATH_IMAGE035
, multiply each other and directly calculate
Figure 395173DEST_PATH_IMAGE040
Step 3:Utilize the intermediate object program vector
Figure 790383DEST_PATH_IMAGE041
And input information bits vector in the check matrix
Figure 667072DEST_PATH_IMAGE038
And check matrix In
Figure 818884DEST_PATH_IMAGE013
Big ring property, the compute codeword vector As follows:
Figure 250445DEST_PATH_IMAGE044
Step 4:: the result with step 3 merges with step 1, finally obtains coding codeword
Beneficial effect:Main innovate point of the present invention is that according to dimension be the characteristics that 2 variable node constitutes big ring, is choosing a variable node arbitrarily and is intercepting one bar limit on big ring, makes coding can be fully directly calculate according to the connecting relation of check matrix like this and finishes.
Be mainly reflected in the following aspects:
1) the LDPC sign indicating number after the structural modifications is little than original LDPC sign indicating number change, limit of amputation
Operation make that performance does not have to change substantially, and the decoding design still can be continued to use accurate loop structure and come effectively-4-
Carry out;
2) need not that check matrix is carried out Gauss and eliminate variation and can encode, because the low-density characteristic of LDPC code check matrix makes encoder complexity low.
Description of drawings
Fig. 1 is to be the macrocyclic structure that 2 submatrix forms by the variable dimension in the class quasi-cyclic LDPC code check matrix.
All explanation of symbols:
The abbreviation of LDPC:Low-Density Parity-Check, low density parity check code;
: the check matrix of original LDPC sign indicating number;
Figure 63046DEST_PATH_IMAGE042
: the check matrix of LDPC sign indicating number after the structural modifications;
Figure 586431DEST_PATH_IMAGE009
: the LDPC code check matrix is corresponding to the submatrix of information bit;
Figure 813013DEST_PATH_IMAGE011
: corresponding to code word one-dimensional degree (column weight is 1) check bit part;
Figure 54639DEST_PATH_IMAGE013
: corresponding to two dimension (column weight is 2) the check bit parts of code word;
Figure 657659DEST_PATH_IMAGE019
: amended pair of dimension check matrix;
Figure 35550DEST_PATH_IMAGE046
: the input vector of encoder;
Figure 636296DEST_PATH_IMAGE047
: the output of encoder, coding codeword vector;
: corresponding to the coded vector of one-dimensional degree check matrix;
Figure 7814DEST_PATH_IMAGE030
: corresponding to the coded vector of two dimension check matrixes;
Figure 302529DEST_PATH_IMAGE018
:
Figure 74176DEST_PATH_IMAGE017
In " 1 " residing position, according to the coordinate of counterclockwise order in this matrix of big ring.
Embodiment
Quasi-cyclic low-density parity check codes of the present invention is optional limit on 2 the big ring in dimension, and it is clipped, and also promptly fills out 0 in the relevant position of low-density check matrix, thereby obtains this a kind of correcting principle of encoding.If the check matrix of original coding can be divided into 3 parts:
Figure 24814DEST_PATH_IMAGE008
, and two dimension check matrix
Figure 969636DEST_PATH_IMAGE017
All " 1 " constitutes a big ring.If
Figure 322120DEST_PATH_IMAGE017
In " 1 " be followed successively by according to the coordinate of counterclockwise order in this matrix of big ring
Figure 326985DEST_PATH_IMAGE018
Structural modifications method concrete steps are: formulate two dimension check matrixes arbitrarily
Figure 764920DEST_PATH_IMAGE017
In one " 1 ", it is changed to " 0 ", amended pair of dimension check matrix is designated as
Figure 14898DEST_PATH_IMAGE019
, the loe-density parity-check code that final structure is revised has check matrix:
Figure 221888DEST_PATH_IMAGE020
。
The uniform enconding method of quasi-cyclic low-density parity check codes is utilized low-density check matrix and the direct calculation code of input information bits vector position.At first utilize the input information vector
Figure 335338DEST_PATH_IMAGE048
, the multiplication mutually of doing vector and matrix greater than 2 part with the column weight (also being the variable node dimension) of check matrix obtains middle vector The variable node dimension is 1 coded vector
Figure 547194DEST_PATH_IMAGE021
Vector in the middle of directly intercepting The relevant position obtain; The variable node dimension is 2 coded vector
Figure 955358DEST_PATH_IMAGE022
Then begin to calculate and to get by start bit, two parts coded vector is pieced together final formation coded vector by bit by its big ring property on bipartite graph
Figure 367885DEST_PATH_IMAGE023
The uniform enconding method of quasi-cyclic low-density parity check codes can be expressed as the step of carrying out in the following order:
Step 1:Utilize the input information bits vector
Figure 458201DEST_PATH_IMAGE038
And check matrix
Figure 639783DEST_PATH_IMAGE033
, multiply each other and directly calculate
Figure 658817DEST_PATH_IMAGE049
Step 2:Utilize the input information bits vector
Figure 293061DEST_PATH_IMAGE038
And check matrix
Figure 859171DEST_PATH_IMAGE035
, multiply each other and directly calculate
Figure 223157DEST_PATH_IMAGE050
Step 3:Utilize the intermediate object program vector And input information bits vector in the check matrix
Figure 33167DEST_PATH_IMAGE038
And check matrix
Figure 402968DEST_PATH_IMAGE042
In
Figure 621460DEST_PATH_IMAGE013
Big ring property, the compute codeword vector
Figure 418515DEST_PATH_IMAGE043
As follows:
Figure 27350DEST_PATH_IMAGE044
Step 4:: the result with step 3 merges with step 1, finally obtains coding codeword
Figure 499045DEST_PATH_IMAGE023
Example: the correction of a kind of quasi-cyclic low-density parity check codes of the present invention and uniform enconding method thereof can be passed through
Following example illustrates.If a code length is 6, message length is 2, and code check is that the original checksums matrix of 1/3 the quasi-cyclic LDPC code with implicit node is as follows:
Figure 509727DEST_PATH_IMAGE051
。
This check matrix can resolve into 3 parts
Figure 540000DEST_PATH_IMAGE008
, wherein,
Figure 636132DEST_PATH_IMAGE052
,
Figure 410053DEST_PATH_IMAGE053
,
Figure 275240DEST_PATH_IMAGE054
。
Figure 414098DEST_PATH_IMAGE009
Corresponding to the information bit part of complete code, size is
Figure 59843DEST_PATH_IMAGE010
, do not send on the channel in the present example, thereby be so-called implicit node section;
Figure 575138DEST_PATH_IMAGE011
Corresponding to the code word dimension is 1 check bit part, and size is
Figure 858614DEST_PATH_IMAGE012
Figure 168372DEST_PATH_IMAGE013
Corresponding to the code word dimension is 2 check bit part, and size is
Figure 301413DEST_PATH_IMAGE014
Parameter
Figure 354820DEST_PATH_IMAGE055
, This check matrix Corresponding node constitutes a big ring, as shown in Figure 1.
Structural modifications of the present invention is to choose any to clip a limit on this big ring, also is that " 0 " is filled out in " 1 " of check matrix relevant position, and the position of drawing a circle as Fig. 1 is set to " 0 ", thereby revised Can be write as:
Figure 949432DEST_PATH_IMAGE058
，
Thereby the LDPC code check matrix behind the structural modification can be write as:
Figure 643719DEST_PATH_IMAGE059
。
Its concrete steps of uniform enconding algorithm of LDPC sign indicating number are as follows behind the structural modification:
Step 1:Utilize the input information bits vector And check matrix
Figure 904378DEST_PATH_IMAGE061
, multiply each other and directly calculate
Figure 299587DEST_PATH_IMAGE062
Step 2:Utilize the input information bits vector
Figure 176277DEST_PATH_IMAGE060
And check matrix , multiply each other and directly calculate
Step 3:Utilize the intermediate object program vector
Figure 526989DEST_PATH_IMAGE041
And check matrix
Figure 258185DEST_PATH_IMAGE042
In
Figure 251549DEST_PATH_IMAGE013
Big ring property, the compute codeword vector
Figure 5878DEST_PATH_IMAGE064
Following progressively calculate shown in (
Figure 318391DEST_PATH_IMAGE065
,
Figure 841776DEST_PATH_IMAGE066
):
Figure 333937DEST_PATH_IMAGE067
,
Figure 575563DEST_PATH_IMAGE068
,
Figure 913003DEST_PATH_IMAGE069
,
Figure 556474DEST_PATH_IMAGE070
；
Step 4:: the result with step 3 merges with step 1, finally obtains coding codeword
Figure 891640DEST_PATH_IMAGE023
 
Fig. 1 is to be the macrocyclic structure of 2 submatrix by the variable dimension in a kind of quasi-cyclic LDPC code check matrix.The coordinate of ring each point in matrix is
Figure 682879DEST_PATH_IMAGE071
, wherein
Figure 761693DEST_PATH_IMAGE065
,
Figure 823452DEST_PATH_IMAGE066

Claims (7)

1. quasi-cyclic low-density parity check codes is characterized in that the dimension of this parity check code variable node is divided into 3 classes: dimension is 1, dimension be 2 and dimension greater than 2; Dimension all is an information node greater than 2 variable node, corresponding to information bit to be encoded position, owing to generally do not send on the channel, thereby be referred to as implicit node; Dimension is that 2 variable node just in time forms an end to end big ring on the bipartite graph of corresponding low-density check matrix correspondence.
2. the modification method of a quasi-cyclic low-density parity check codes as claimed in claim 1, it is characterized in that this method is: be optional limit on 2 the big ring in described dimension, it is clipped, also promptly fill out 0, thereby obtain this a kind of correcting principle of encoding in the relevant position of low-density check matrix; The row of filling out 0 operation place in the check matrix is called coding and starts row as the position that coding begins to start.
3. the modification method of quasi-cyclic low-density parity check codes according to claim 2, it is characterized in that described correcting principle is embodied in the modification to the check matrix of low density parity check code, retouching operation is 2 row to the column weight that likes the big ring of formation in the check matrix, appoint " 1 " get row wherein it to be set to " 0 ", the row that displacement takes place is called to start goes, and this correcting principle specifically is expressed as in conjunction with the definition of check matrix:
Definition: a class has the check matrix of implicit node quasi-cyclic low-density parity check codes:
Figure FDA0000040551030000011
Wherein, H I, jBe that size is the cyclic shift permutation submatrix of z * z, this matrix depends on cyclic shift amount, m fully bBe the line number that cyclic shift permutation submatrix in the check matrix accounts for, n bBe the columns that cyclic shift permutation submatrix in the check matrix accounts for, this H oThe size of matrix is m * n=m bZ * m bZ; Be convenient coding, this type of check matrix is divided into 3 parts:
H o＝[H s|H p1|H p2]，
Wherein, H sCorresponding to the information bit part of complete code, size is m * k; One-dimensional degree check matrix H P1Right
-1-
Should be 1 check bit part in code word one-dimensional degree column weight, size be m * n 1Two dimension check matrix H P2Corresponding to the two dimension column weights of code word is 2 check bit part, and size is m * n 2The total length of coding is n=k+n 1+ n 2Because H sCorresponding codes codeword information bit position does not send on the channel, thereby is the loe-density parity-check code with implicit node.
4. the modification method of quasi-cyclic low-density parity check codes according to claim 3 is characterized in that described pair of dimension check matrix H P2All " 1 " constitutes a big ring, establishes two dimension check matrix H P2In " 1 " be followed successively by according to the coordinate of counterclockwise order in this matrix of big ring
Figure FDA0000040551030000021
5. the modification method of quasi-cyclic low-density parity check codes according to claim 3 is characterized in that described pair of dimension check matrix H P2In formulate arbitrarily one of them " 1 ", it is changed to " 0 ", amended pair of dimension check matrix is designated as
Figure FDA0000040551030000022
The loe-density parity-check code of final correcting principle has check matrix:
Figure FDA0000040551030000023
6. the uniform enconding method of a quasi-cyclic low-density parity check codes as claimed in claim 3, it is characterized in that: utilize the low-density check matrix of correcting principle and input information bits vector to calculate bits of coded: at first utilize input information vector s, the multiplication mutually of doing vector and matrix greater than 2 part with the column weight of check matrix obtains middle vector u; The variable node dimension is 1 coded vector
Figure FDA0000040551030000024
Directly the relevant position of vector u obtains in the middle of the intercepting; The variable node dimension is 2 coded vector Then begin to calculate and to get by start bit, two parts coded vector is pieced together final formation coding output vector by bit by its big ring property on bipartite graph
Figure FDA0000040551030000026
7. the uniform enconding method of quasi-cyclic low-density parity check codes according to claim 6 is characterized in that described coded vector separated into two parts carries out, and a part is 1 row corresponding to the check matrix column weight, gets by the dope vector direct coding; Another part is 2 row corresponding to the check matrix column weight, and the respective coding vector can calculate by bit by big ring property and get, and this encryption algorithm specifically is expressed as the several steps of execution in the following order:
Definition: the input vector of establishing encoder is s=(s 1, s 2, L, L, s k), k=k wherein bZ; Encoder is output as coding codeword, is designated as
Figure FDA0000040551030000027
If the corresponding implicit node of information bit, then information bit does not send, and encoder is output as
Figure FDA0000040551030000028
Wherein,
Figure FDA0000040551030000029
Corresponding to the coded vector of one-dimensional degree check matrix, its size is made as n 1:
Figure FDA0000040551030000031
Corresponding to the coded vector of two dimension check matrixes, its size is made as n 2With matrix H sWrite as matrix in block form
Figure FDA0000040551030000032
H wherein S1Size be n 1* k, H S2Size be (m-n 1) * k, and m-n 1=n 2
Step 1: utilize input information bits vector s=[s 1, s 2, L, s k] and check matrix H S1, multiply each other and directly calculate
Figure FDA0000040551030000033
Step 2: utilize input information bits vector s=[s 1, s 2, L, s k] and check matrix H S2, multiply each other and directly calculate
Figure FDA0000040551030000034
Step 3: utilize input information bits vector s=[s in intermediate object program vector u and the check matrix 1, s 2, L, s k] and check matrix H in H P2Big ring property, the compute codeword vector
Figure FDA0000040551030000035
As follows:
Step 4:: the result with step 3 merges with step 1, finally obtains coding codeword
Figure FDA0000040551030000037
CN2010106058385A 2010-12-24 2010-12-24 Quasi-cyclic low-density parity-check (QC-LDPC) code and correcting and linear coding method thereof Pending CN102055485A (en)

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