WO2013023604A1

WO2013023604A1 - Ldpc code check matrix construction method and device, and encoding method and system

Info

Publication number: WO2013023604A1
Application number: PCT/CN2012/080188
Authority: WO
Inventors: 李继龙; 白栋; 高鹏; 申红兵; 邢观斌; 冯昂
Original assignee: 国家广播电影电视总局广播科学研究院; 北京泰美世纪科技有限公司
Priority date: 2011-08-17
Filing date: 2012-08-15
Publication date: 2013-02-21
Also published as: CN102957435A; CN102957435B

Abstract

Proposed is an LDPC code check matrix construction method, including: constructing an MB × NB-dimension transition basis matrix (BT) of LDPC code which has a production code rate R and code length N, where MB = M/K, NB = N/K, M = N(1 - R), K is the divergence ratio of the transition basis matrix, k∈Φ, and Φ is a set of the common factors of M and N; using a K × K-dimension matrix to replace the elements of the transition basis matrix (BT), and expanding the transition basis matrix (BT) to an M × N-dimension transition matrix (HT); and removing at least one element "1" of at least one K × K-dimension matrix of the transition matrix (HT) to obtain a check matrix (H), wherein the check matrix (H) has an optimized row redistribution and/or column redistribution used for encoding and/or decoding the LDPC code. Also proposed are an LDPC code check matrix construction device, and an encoding method and system.

Description

Method, device and coding method and system for LDPC code check matrix

The present invention relates to the field of wireless communications, and in particular, to a method, apparatus, and method and system for constructing a low density parity check (LDPC) code check matrix. Background technique

In the famous "Mathematical Theory of Communication", Shannon clarified that the way to achieve reliable transmission in noisy channels is coding. He proposed the maximum rate at which information can be transmitted in a noisy channel, namely the channel capacity. It also derives the minimum signal-to-noise ratio required for error-free transmission of information, known as the Shannon limit. Although Shannon's channel coding theory gives the ultimate performance of optimal coding, it does not give a specific coding scheme. Based on this, people have been working hard to find a coding scheme that is close to the Shannon limit in performance.

The LDPC code was first proposed by Gallager and is a linear block code with a very sparse check matrix. That is to say, there are only a very small number of non-"0" elements in the check matrix (for binary codes, non-"0" elements are "1" elements). Further research by Mackay et al. shows that the performance of LDPC codes can approach the Shannon limit under the message passing (MP) iterative decoding algorithm.

Currently, LDPC codes are being used more and more in various communication systems. The China Mobile Multimedia Broadcasting (CMMB) system uses the channel coding scheme of the LDPC code. The CMMB system realizes large-area broadcast coverage of the world by satellite and terrestrial base stations, and transmits multi-channel audio and video broadcasting services. Users can use the terminal to achieve mobile reception. Due to the limited power of the satellite signal, the synchronous satellite orbit is at an altitude of 36,000 km, and the path loss of the downlink signal is severe, resulting in a small link margin of the receiving terminal. Therefore, it is necessary to design an LDPC code with excellent performance. In addition, the actual communication system requires low coding and decoder implementation complexity. Although the method of computer search can generate LDPC codes with excellent performance randomly or randomly, but due to the randomness of the check matrix, a large amount of memory is required to store them. Since the code length of the LDPC code is long, the implementation of the encoder is very complicated. Since the code length of the LDPC code is long, the implementation of the encoder is very complicated.釆 Using mathematical methods to construct the LDPC code, you can add a certain constraint to make the check matrix have a certain structure.

Moreover, the number of "1"s in each row of the check matrix is called the "line" of the row, and the number of "1"s in each column of the check matrix is called the "column" of the column. If the following conditions are met: all rows of the check matrix have the same row degree and the column degrees of all columns are the same, then the LDPC code is called a regular LDPC code.

LDPC code. Some research shows that non-ijLDPC^ horse performance is better than see ^ (code. One of the important methods to optimize irregular LDPC codes is to optimize the distribution of row and column degrees.

The quasi-cyclic LDPC code is widely used because it reduces the complexity of the codec. In order to get the knot The design of the quasi-cyclic LDPC code divides the entire check matrix into square sub-arrays. Each sub-array usually becomes a "block", and each sub-array satisfies the definition of the cyclic matrix. Generally, the line distribution and the column degree distribution of the LDPC code of the finite code length are approximations to the preference distribution, and the degree distribution of the quasi-cyclic LDPC code often cannot be obtained accurately due to the "blocking" structure of the quasi-cyclic LDPC code. Approximation, which affects the performance of the code set. Summary of the invention

The present invention aims to at least solve or alleviate one of the above technical defects, in particular, by using the check matrix construction method of the LDPC code proposed by the present invention, constructing an LDPC code with excellent performance at an arbitrary bit rate, and solving the storage problem of the check matrix. , effectively reduce the implementation complexity of the encoder.

In order to achieve the above object, an aspect of the present invention provides a method for constructing an LDPC code check matrix, which includes the following steps:

Construct an over-basic matrix BT of ΜΒχΝΒV LDPC codes with a code rate R and a code length of N, where MB=M/K, NB=N/K, M = N ( 1 - R ), K is an excessive basis The expansion ratio of the matrix, KG Φ, Φ is the set of common factors of M and N;

Substituting the elements of the excess basic matrix BT with the matrix of the K X K dimension, expanding the excessive basic matrix BT into the MxN dimensional excess matrix HT;

Removing at least one element "1" of the matrix of at least one KXK dimension in the over matrix HT to obtain a test matrix H having an optimized row redistribution and/or column redistribution for performing LDPC codes Encoding and / or decoding.

Another aspect of the present invention provides an apparatus for constructing an LDPC code check matrix, comprising an excessive base matrix construction unit, an excessive matrix expansion unit, and a check matrix generation unit, wherein:

An over-basic matrix construction unit for constructing an over-basic matrix BT of an MBxNB dimension of an LDPC code having a code rate R and a code length N, where MB=M/K, NB=N/K, M=N (1) - R ), K is the expansion ratio of the excess base matrix, and Φ is the set of common factors of Μ and Ν;

An over-matrix expansion unit for replacing an element in the excess base matrix ΒΤ with a matrix of Κ X Κ dimension, and expanding the excessive base matrix ΒΒ to an excessive matrix HB of the MxN dimension;

a check matrix generation unit for removing at least one element "1" of at least one KK-dimensional matrix in the over matrix HB to obtain a test matrix H having an optimized row redistribution and/or column redistribution For performing encoding and/or decoding of the LDPC code.

Another aspect of the present invention also provides an encoding method of an LDPC code, comprising the following steps: dividing a check matrix H into two sub-matrices H=[HmHp], where Hm is a sub-matrix of Mx(N_M) dimensions, Hp For the sub-matrices of the MxM dimension, Hp-1 and Hp-lHm are calculated, and the check matrix H is obtained by:

Construct an over-basic matrix of ΜΒχΝΒV LDPC codes with a code rate of R and a code length of N BT, where MB=M/K, NB=N/K, M = N ( 1 - R ), K is the expansion ratio of the excess basic matrix, ≡Φ, Φ is the set of common factors of Μ and Ν;

Substituting the elements of the excess base matrix ΒΤ with the matrix of Κ X Κ dimension, expanding the excess base matrix ΒΤ into the 矩阵 dimension of the matrix ΗΤ;

Removing at least one element "1" of the matrix of at least one ΚX Κ dimension of the over matrix ΗΤ to obtain a test matrix Η having an optimized row weight distribution and/or column redistribution for performing LDPC Encoding and/or decoding of a code.

Another aspect of the present invention also provides an encoding system for an LDPC code, comprising: an LDPC code check matrix construction apparatus, an encoding matrix storage unit, a check sequence calculation unit, and a codeword sequence generation unit,

An apparatus for constructing an LDPC code check matrix, configured to construct an over-basic matrix BT of an MB xNB dimension of an LDPC code having a code rate R and a code length N, where MB=M/K, NB=N/K, M = N ( 1 - R ), K is the expansion ratio of the excess base matrix, ΚΕ Φ , Φ is the set of common factors of Μ and Ν, and replaces the elements in the excess base matrix Κ with the matrix of Κ Κ dimension, and the excessive basic matrix ΒΤ expanding into an over-matrix ΜχΝ of the dimension, removing at least one element "1" of the matrix of at least one ΚX Κ dimension of the over-matrix , to obtain a test matrix ΜχΝ of the dimension;

The coding matrix storage module is configured to store the structure of the coding matrix, and divide the check matrix H of the MxN dimension constructed by the construction device of the LDPC code check matrix into two sub-matrices H=[HmHp], where Hm is Μχ(Ν-Μ) a sub-matrix of a dimension, Hp is a sub-matrix of a dimension, the coding matrix storage module is configured to store a structure of a matrix Hp-lHm, and the Hp-lHm has a structure of a block-by-loop, and can be stored in units of blocks;

a check sequence calculation module, configured to multiply the input information sequence m by a matrix (Hp-lHm) T to obtain a check sequence p;

A codeword sequence generating module is configured to combine the information sequence m and the check sequence p into a codeword sequence c and output.

The technical solution proposed by the present invention can construct an LDPC code with excellent performance at an arbitrary code rate. Furthermore, the technical solution proposed by the present invention also solves the storage problem of the check matrix, and effectively reduces the implementation complexity of the encoder. The LDPC code constructed by the technical solution proposed by the present invention can be fully compatible with the physical layer structure of the CMMB system, and can effectively improve the link margin of the system.

Moreover, the technical solution proposed by the present invention also solves the problem of the degree distribution of the quasi-cyclic LDPC code and enhances the performance of the code set.

The additional aspects and advantages of the invention will be set forth in part in the description which follows. DRAWINGS The above and/or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments in conjunction with the accompanying drawings in which: FIG. FIG. 3 is a schematic diagram of the expansion of the excess base matrix BT into the excess matrix HT according to the second embodiment of the present invention; FIG. 4 is a schematic structural diagram of the apparatus for constructing the LDPC code check matrix according to the first embodiment of the present invention; Schematic diagram of the coding system of the LDPC code of the embodiment of the invention;

Figure 6 is a schematic diagram of simulation of Embodiment 1 of the present invention. detailed description

The embodiments of the present invention are described in detail below, and the examples of the embodiments are illustrated in the drawings, wherein the same or similar reference numerals are used to refer to the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the drawings are intended to be illustrative of the invention and are not to be construed as limiting.

In order to achieve the object of the present invention, an embodiment of the present invention proposes a construction method of an LDPC code check matrix.

As shown in Figure 1, the following steps are included:

S101: Constructing an over-basic matrix ΜΒχΝΒ of a dimension of an LDPC code having a code rate R and a code length N, where ΜΒ=Μ/Κ, ΝΒ=Ν/Κ, Μ = Ν ( 1 - R ), K is The expansion ratio of the excess basic matrix, ΚΕ Φ, Φ is the set of common factors of Μ and Ν.

Specifically, constructing an overtone basis matrix BT of an MBxNB dimension of an LDPC code having a code rate R and a code length of N includes the following steps:

Constructing an over-basic matrix BT of MB NB dimension, selecting the number of Γ in each row and each column of the excess base matrix BT, so that the row weight and column redistribution of BT satisfy a predetermined node degree distribution; the row weight and the column weight Under the premise that the predetermined node degree distribution is satisfied, the position of "1" in each row and each column in the excess base matrix BT is selected, so that the sub-matrix of the MBxMB dimension composed of the latter MB columns of BT is full rank.

The structure of the excessive basic matrix BT can be stored in the form of a table, and each row of the table records the position of the Γ in each row of the BT. The order of the rows can be arbitrary, and the constructed BT is equivalent.

S102: Substituting the element in the excess basic matrix BT with the matrix of the K x K dimension, and expanding the excessive basic matrix BT into the excessive matrix HT of the dimension.

In one embodiment, expanding the excessive base matrix BT includes the following steps: replacing "0" in the excessive base matrix BT with the all-"0" matrix Z of the KXK dimension, and using "1" in the BT ΚχΚV's cyclic permutation matrix P is replaced, where the row number i and the column number j of "1" in P satisfy j=(i+k) modK, k is the offset of the cyclic permutation matrix, and mod represents the modulo operation; Choose an offset for each cyclic permutation matrix p.

In another embodiment, expanding the excessive base matrix BT includes the following steps: replacing "0" in the excessive base matrix BT with the all-"0" matrix K of the KXK dimension, and "1" in the ΒΤ Substituting the algebraic permutation matrix ΚχΚ of ΚχΚ dimension, where the row number i and the column number j of "1" in Ρ satisfy j=f(i), where f(i) is a permutation polynomial over a finite field or a ring;

Choose an offset for each algebraic permutation matrix P.

The offset of the cyclic permutation matrix P and the algebraic permutation matrix P may be stored in the form of a table, and each row of the table records the offset of the cyclic permutation matrix corresponding to "1" in each row of the basic matrix BT. The offset of the same row is added to the same offset q, that is, k'=(k+q;) modK, and the constructed HT is equivalent.

S103: removing at least one element "1" of the matrix of at least one KK dimension in the over matrix HT to obtain a test matrix H having an optimized row weight distribution and/or column redistribution for performing LDPC Encoding and/or decoding of a code.

Specifically, in the excess matrix HT, for some of the Κ χ dimension expansion matrices, some of the elements "1" are removed, the degree distribution of the Η is optimized, the target degree distribution is approximated, the check matrix 获得 is obtained, and then the check is performed. The matrix Η can be used for encoding or decoding of LDPC codes.

In one embodiment, for the permutation matrix Ρ, r consecutive "1"s of row numbers are selected and deleted from the over-matrix HT to obtain a check matrix H, where 0 < r ≤ K.

In another embodiment, for the permutation matrix P, r consecutive "1"s of column numbers are selected and deleted from the excess matrix HT to obtain a check matrix H, where 0 < r ≤ K.

Moreover, in another embodiment, for the permutation matrix P, r "1"s are randomly selected and deleted from the excess matrix HT to obtain a check matrix H, where 0 < r ≤ K.

Thus, the structure of the check matrix H can be stored in the form of a base matrix position table and a cyclic permutation matrix offset table, thereby solving the storage problem of the check matrix.

Based on the above analysis, an embodiment of the present invention also proposes a method of encoding an LDPC code constructed according to the construction method of the check matrix, which includes the following steps:

The above-mentioned MxN-dimensional check matrix H is divided into two sub-matrices 11=[13⁄4111^], where Hm is

子(Ν-Μ) dimension submatrix, Hp is a subdimension of ΜχΜ dimension, calculate Ηρ-1 and Hp-lHm;

Calculate the check sequence p=m(Hp-lHm)T of the dimension based on the input information sequence m of the χ(Ν-Μ) dimension;

The information sequence m and the check sequence p are combined into a 1 x N-dimensional codeword sequence c = [mp] and output.

In order to further illustrate the present invention, an embodiment in which the present invention is applied to a CMMB system will be described below in conjunction with the physical layer structure of the CMMB system.

Specific embodiment 1:

Construct an LDPC code with a code rate of 1/2 for the CMMB system. In order to be compatible with the physical layer structure of the CMMB system, the code length N is chosen to be 9216, that is, a check matrix H of 4608x9216 dimensions is constructed. The set Φ of the common factors of 4608 and 9216 is calculated. To be compatible with the 1/2 and 3/4 code rate LDPC codes in the CMMB system, the expansion ratio K is chosen to be 256. Thus, the dimension of the excessive base matrix BT is 18x36.

Select the row redistribution and column redistribution of the check matrix H. Preferably, the row weight distribution of H is

{λ7, λ8, λ9, λ10}={17/288,223/288,1/18,2/18} , the column redistribution is

{ρ15,ρ14,ρ5,ρ4,ρ3,ρ2}={7/64,1/576,1/9,1/36,5/18,17/36}„

Since the expansion ratio is chosen to be 256, only partial row redistribution and column redistribution can be adapted. After calculation, define the matrix of the excess matrix ΗΤ 重重重重

{λ7, λ8, λ9, λ10}={1/18,14/18,1/18,2/18}, the column redistribution is

{ρ15, ρ5, ρ4, ρ3, ρ2} = {4/36, 4/36, 1/36, 10/36, 17/36}.

Under the premise of satisfying the row weight and column weight distribution, arbitrarily select the position of the Γ in each row and each column of the base matrix 过度 of the over matrix ,, but guarantee that the 18×18-dimensional sub-matrix consisting of the last 18 columns of ΒΤ is full Rank.

Replace "0" in the base matrix 过度 of the over matrix 用 with the 256x256-dimensional all "0" matrix ,, and replace the "1" in ΒΤ with the 256x256-dimensional cyclic permutation matrix , to obtain the over matrix ΗΤ. The line number i and the column number j of "1" in Ρ satisfy j=(i+k) mod256, where k is the offset of the cyclic permutation matrix.

Among them, the offset of each cyclic permutation matrix P is arbitrarily selected. The offset is appropriately adjusted to have an optimized stop set.

Then, according to the calculation, the cyclic permutation matrix P corresponding to some elements in the basic matrix BT of the excessive matrix HT is adjusted, and successive numbers are selected, and all the elements are set to zero, thereby obtaining the line degree satisfying the optimization. And the check matrix H of the distribution of the degree.

More specifically, an optimized design of H is expressed as:

0: (1, 239, 0) (4, 166, 0) (5, 247, 0) (11, 31, 0) (12, 217, 0) (14, 72, 0) (18, 192, 0) (19, 0, 0) 1 : (2,251,0)(5,153,0)(11,159,0χ200)(14,48,0)(15,31,0)(19,0,0)(20,0,0)

2: (5,230,0)(6,182,0)(11 ,91,0)(14,62,0)(16,170,0)(20,0,0)(21,0,0)

3 :(2,255,0)(3,196,0)(5,171,0)(7,26,0)(10,1 1,0)(12,71 ,0)(17,51,0)(21,0 ,0) (22,0,0)

4: (4,240,0)(5,66,0)(11,0,0)(14,1 18,0)(17,39,0)(22,0,0)(23,0,0)

5: (2,212,0)(3,1 15,0)(5,93,0)(8,210,0)(9,29,0)(14,249,0)(18,39,0)(23,0 ,0) (24,0,0)

6:(3,60,0)(5,46,0)(1 1,40,0)(13,180,0)(17,192,0)(24,0,0)(25,0,0)

7: (4,1,0)(10,247,0)(11,142,0)(14,210,0)(16,192,0)(25,0,0)(26,0,0)

8: (5,66,0)(10,208,0)(11 ,31,0)(14,116,0)(15,20,0)(26,0,0)(27,0,0)

9:(2,47,0)(6,8,0)(10,40,0)(11,219,0)(17,148,0)(27,0,0)(28,0,0) 10: (5, 248, 0) (6, 255, 0) (11, 55, 0) (14, 56, 0) (16, 201, 0) (28, 0, 0) (29, 0, 0) 11: (2, 231, 0)(5,83,0)(7,38,0)(9,87,0)(14,245,0)(17,194,0)(29,0,0)(30,0,0) 12:( 9,249,0)(11,93,0)(13,83,0)(14,20,0)(30,0,0)(31,0,0)

13:(5,39,0)(8,76,0)(11,225,0)(14,185,0)(15,118,0)(31,0,0)(32,0,0)

14: (5,81,0)(9,182,0)(10,248,0)(11,68,0)(14,23,0)(32,0,0)(33,0,0)

15: (1,183,0)(5,111,0)(11,230,0)(12,246,0)(14,105,0)(33,0,0)(34,0,0)

16:(5,87,0)(8,244,0)(9,183,0)(11,139,0)(14,141,0)(34,0,0)(35,0,0)

17:(5,153,0)(7,238,0)(11,80,0)(13,92,0)(14,75,0)(18,48,0)(35,0,0)

For the above design, each row is the expansion and adjustment parameters of the base matrix 过度 of the matrix. The triplet (col, shift, adj(16)) indicates that the col column of the row is a cyclic permutation matrix with an offset of shift.

P replacement. Adj(16) represents a four-bit unsigned hexadecimal number with a total of 16 bits, each of which represents the adjustment scheme of P's 16 lines. Definition adj(2) represents a sixteen-bit unsigned binary number whose value is equal to adj(16). When a bit of adj(2) is "1", it means that all 16 lines corresponding to this bit are set to "0", otherwise it will not change. The correspondence is: the ith bit of adj(2), which controls the ixth 16th row to the ixth 16+15th row of the cyclic permutation matrix P.

For example, when adj(16)=0x0001, all elements on the 0th to 15th lines are set to zero. When adj(16) = 0xC000, all elements on the 240th line to the 255th line are set to zero. Fig. 2 is a schematic diagram showing the expansion of the excessive basic matrix BT into the excessive matrix HT according to the first embodiment of the present invention. Figure 2 is an illustration of the third element adj(16) in the triple (col, shift, adj(16)). The following steps: ' ' ' ' a ' , , , , , and the above-mentioned 4608x9216-dimensional check matrix H is divided into two sub-matrices H=[HmHp], where Hm is

The sub-matrix of the 4608x4608 dimension, Hp is a sub-matrix of 4608x4608 dimensions, and Hp-1 and Hp-lHm are calculated, and the matrix Hp-lHm has a structure of a block cycle;

Calculating a check sequence p=m(Hp-lHm)T according to the input information sequence m;

The information sequence m and the check sequence p are combined into a codeword sequence c=[mp] and output.

According to the Shannon channel coding theory, after applying the embodiment of the present invention, the 1/2 code rate error correction coding has a signal-to-noise ratio (SNR) limit of about 0.2 dB when the bit error rate (BER) reaches 10-4. The 1/2 code rate LDPC code constructed in Embodiment 1 has an SNR of about l.ldB when the BER reaches 10-4, and has excellent performance close to the theoretical limit.

Specific embodiment 2:

Construct an LDPC code with a code rate of 3/4 for the CMMB system.

In order to be compatible with the physical layer structure of the CMMB system, the code length N is chosen to be 9216, that is, a check matrix H of 2304x9216 dimensions is constructed.

Calculate the set Φ of the common factors of 2304 and 9216, and select the appropriate expansion ratio ΚΕΦ. In order to The 1/2 and 3/4 code rate LDPC codes in the CMMB system are compatible, and the expansion ratio is 256. Thus, the dimension of the base matrix BT is 9x36.

Select the row redistribution and column redistribution of the check matrix H.

Preferably, the row weight distribution of H is {λ16, λ15, λ14}={15/144, 1/144, 8/9}, and the column weight distribution is {ρ9, ρ8, ρ5, ρ4, ρ3, ρ2}={ 35/576,1/576,1/9,2/9,7/18,2/9}„

Since the expansion ratio is chosen to be 256, only partial row redistribution and column redistribution can be adapted. After calculation, the basic matrix defining the over-matrix ΗΤ is redistributed to {λ16, λ14}={1/9,8/9}, and the column redistribution is {ρ9, ρ5, ρ4, ρ3, ρ2}={1/ 18, 1/9, 2/9, 7/18, 2/9}.

Under the premise of satisfying the row weight and column weight distribution, the position of "1" in each row and each column of the base matrix 过度 of the over matrix 任意 is arbitrarily selected, but the 9×9-dimensional sub-matrix consisting of the last 9 columns of ΒΤ is guaranteed to be full. rank.

The offset of each cyclic permutation matrix P is arbitrarily chosen. The offset is appropriately adjusted to have an optimized stop set.

Then, according to the calculation, the cyclic permutation matrix P corresponding to the element part elements in the base matrix BT of the excess matrix HT is adjusted, and consecutive numbers of the rows are selected, and all the elements are set to zero to obtain the row and column satisfying the optimization. The check matrix H of the degree distribution.

Specifically, an optimized design of H is expressed as:

0: (1,150,0)(2,223,0)(6,246,0)(8,236,0)(10,236,0)(11,78,0)(13,137,0)(17,48,0)

(18,23,0)(20,195,0)(23,87,0)(25,194,0)(27,60,0)(28,0,0)

1 :(4,188,0)(8,212,0)(10,202,0)(11,213,0)(13,252,0)(15,150,0)(18,205,0)

(20,146,0)(21,234,0)(23,207,0)(25,15,0)(28,0,0)(29,0,0)

2:(4,243,0)(7,241,0)(9,0,0)(11,254,0)(13,17,0)(16,237,0)(17,254,0)(18,18,0)

(21,111,0)(23,235,0)(25,25,0)(29,0,0)(30,0,0)

3:(2,137,0)(5,243,0)(9,255,0)(11,255,0)(13,210,0)(14,6,0)(18,162,0)(19,243,0) (21,119,0)( 23,4,0)(26,5,0)(30,0,0)(31,0,0)

4: (4, 141, 0) (7, 252, 0) (9, 70, 0) (13, 163, 0) (14, 4, 0) (15, 78, 0) (17, 242, 0) (19, 106, 0) (23 ,12,0)(24,212,0)(26,20,0)(31,0,0)(32,0,0)

5: (3, 225, 0) (6, 109, 0) (8, 154, 0) (13, 128, 0) (14, 244, 0) (15, 170, 0) (19, 148, 0) (20, 3, 0) (23, 85, 0 )(24,183,0)(27,211,0)(32,0,0)(33,0,0)

6:(2,247,0)(3,252,0)(7,246,0)(8,226,0)( ll,251,0)(12,251,0)(13,222,0x400) (15,182,0)(17,186,0)( 19,3,0)(22,199,0)(23,199,0)(26,199,0)(33,0,0)(34,0,0) 7:(5,250,0)(6,62,0)( 7,150,0)(10,158,0)(12,250,0)(13,90,0)(16,3,0)(19,111,0) (22,207,0)(23,39,0)(25,199,0)(34,0,0)(35,0,0)

8: (1,49,0)(5,229,0)(10,255,0)(12,254,0)(13,227,0)(15,69,0)(16,98,0)(20,70,0) (22,197,0)(23,208,0)(24, 199,0)(27, 199,0)(35,0,0)

For the above design, each row is the expansion and adjustment parameters of the base matrix 过度 of the matrix. The triplet (col, shift, adj(16)) is represented by the cyclic permutation matrix P replacement of the row col column with the offset being shifted. Adj(16) represents a four-bit unsigned hexadecimal number with a total of 16 bits, each representing a 16-line adjustment scheme for P. Definition adj(2) represents a sixteen-bit unsigned binary number whose value is equal to adj(16). When a bit of adj(2) is "Γ", it means that all 16 lines corresponding to this bit are set to "0", otherwise they are unchanged. The corresponding relationship is: the i-th bit of adj(2), which controls the number of the cyclic permutation matrix P From line 16 to line i x 16+15.

For example, when adj(16)=0x0001, all elements on the 0th to 15th lines are set to zero. When adj(16) = 0xC000, all elements from line 240 to line 255 are set to zero. Fig. 3 is a schematic diagram showing the expansion of the excessive basic matrix BT into the excessive matrix HT according to the second embodiment of the present invention. Figure 3 is an illustration of the third element adj(16) in the triple (col, shift, adj(16)). The following steps: ' ' ' ' a ' , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , calculating Hp-1 and Hp-lHm, and the matrix Hp-lHm has a structure of a block cycle;

Calculating a check sequence p=m(Hp- lHm)T according to the input information sequence m;

The information sequence m and the check sequence p are combined into a codeword sequence 0 = [11^] and output.

Based on the above analysis, an embodiment of the present invention also proposes an apparatus for constructing an LDPC code check matrix. 4 is a schematic structural diagram of an apparatus for constructing an LDPC code check matrix according to an embodiment of the present invention.

As shown in FIG. 4, the apparatus includes an excessive base matrix construction unit 410, an excessive matrix expansion unit 420, and a check matrix generation unit 430, where:

The over-basic matrix construction unit 410 is configured to construct an over-basic matrix BT of an MBxNB dimension of an LDPC code having a code rate R and a code length N, where MB=M/K, NB=N/K, M=N ( 1 - R ), K is the expansion ratio of the excess basic matrix, and Φ is the set of common factors of Μ and Ν;

The excess matrix expansion unit 420 is configured to replace the elements in the excess basic matrix ΒΤ with the matrix of Κ X Κ dimension, and expand the excessive basic matrix ΒΤ into the 矩阵 dimension of the excess matrix ΗΤ;

The check matrix generating unit 430 is configured to remove at least one element "1" of the matrix of at least one of the ΗΤ Κ matrix of the over matrix ΗΤ, to obtain a check matrix Η, the check matrix Η having an optimized row redistribution and/or column Redistribution, used to encode and/or decode LDPC codes.

In one embodiment, the excessive base matrix construction unit 410 is configured to construct an excessive base matrix BT of an MBxNB dimension, and select the number of "1"s in each row and each column of the excessive base matrix BT. The row weight and column weight distribution of BT satisfy a predetermined node degree distribution; and under the premise that the row weight and the column weight satisfy a predetermined node degree distribution, the position of "1" in each row and each column in the excessive base matrix BT is selected. , making the sub-matrix of the MBxMB dimension composed of the last MB column of BT full rank.

In one embodiment, the excess matrix expansion unit 420 is configured to replace "0" in the excessive base matrix BT with the all-"0" matrix K of the KXK dimension, and use the "1" in the ΚΧΚ for the cyclic permutation matrix of the dimension ΡReplace, where 行 "" line number i and column number j satisfy j=(i+k) modK, k is the offset of the cyclic permutation matrix, mod represents the modulo operation; and for each cyclic permutation matrix P selects an offset.

In one embodiment, the over matrix expansion unit is configured to replace "0" in the excessive base matrix BT with the all-zero matrix K of the KXK dimension, and replace the "1" in the ΚΧΚ with the algebraic substitution matrix of the dimension Ρ In place, where the row number i and the column number j of "1" in the 满足 satisfy j=f(i), where f(i) is a permutation polynomial over a finite field or a ring; and select one for each algebra permutation matrix P Offset.

As shown in FIG. 5, an embodiment of the present invention further provides an LDPC code coding system, including an LDPC code check matrix construction apparatus 510, an encoding matrix storage unit 520, a check sequence calculation unit 530, and a codeword sequence generation. Unit 540, wherein:

An apparatus 510 for constructing an LDPC code check matrix is configured to construct an over-basic matrix BT of a dimension of an LDPC code having a code rate R and a code length N, where ΜΒ=Μ/Κ, ΝΒ=Ν/Κ, Μ = Ν ( 1 - R ), K is the expansion ratio of the excess base matrix, ΚΕ Φ, Φ is the set of common factors of Μ and Ν, and replacing the elements in the excess base matrix Κ with the matrix of Κ X Κ The matrix ΒΤ is expanded into an 过度-dimensional over-matrix ΗΤ, and at least one element "1" of the matrix of at least one ΚX Κ dimension in the over-matrix ΗΤ is removed to obtain a test matrix ΜχΝ of the ΜχΝ dimension;

The coding matrix storage module 520 is configured to store the structure of the coding matrix, and divide the check matrix H of the MxN dimension constructed by the construction device of the LDPC code check matrix into two sub-matrices 11=[13⁄4111^], where Hm is Μχ(Ν - Μ) a sub-matrix of dimensions, Hp is a sub-matrix of the dimension, the coding matrix storage module is used to store the structure of the matrix Hp-lHm, and the Hp-lHm has a structure of a block-loop, which can be performed in units of blocks Storage

The check sequence calculation module 530 is configured to multiply the input information sequence m by the matrix (Hp-lHm)T to obtain a check sequence p; since Hp-lHm has a structure of a block cycle, matrix multiplication m (Hp-lHm) T can be implemented in a simple manner, such as a shift register, thereby greatly reducing the implementation complexity of the encoder;

The codeword sequence generating module 540 is configured to combine the information sequence m and the check sequence p into a codeword sequence c and output.

As an embodiment of the above encoding device:

The code rate R is 1/2, the code length N is 9216, the expansion ratio is 10^7256, and the line weight distribution of the excessive base matrix BT is {λ7, λ8, λ9, λ10}={1/18, 14/18, 1/ 18,2/18}, the column is redistributed as

{ρ15, ρ5, ρ4, ρ3, ρ2}={4/36, 4/36, 1/36, 10/36, 17/36}; The row weight distribution of H is { λ 7, λ 8, λ 9, λ 10}={17/288, 223/288, 1/18, 2/18}, and the column weight distribution is { ρ 15, ρ 14, ρ 5, ρ 4, ρ 3, ρ 2}={7/64, 1/576, 1/9, 1/36, 5/18, 17/36};

Check matrix Η is specifically:

2: (5,230,0)(6,182,0)(11 ,91,0)(14,62,0)(16,170,0)(20,0,0)(21,0,0)

4: (4,240,0)(5,66,0)(11,0,0)(14,1 18,0)(17,39,0)(22,0,0)(23,0,0)

6:(3,60,0)(5,46,0)(1 1,40,0)(13,180,0)(17,192,0)(24,0,0)(25,0,0)

7: (4,1,0)(10,247,0)(11,142,0)(14,210,0)(16,192,0)(25,0,0)(26,0,0)

8: (5,66,0)(10,208,0)(11 ,31,0)(14,116,0)(15,20,0)(26,0,0)(27,0,0)

9:(2,47,0)(6,8,0)(10,40,0)(11,219,0)(17,148,0)(27,0,0)(28,0,0)

10: (5, 248, 0) (6, 255, 0) (11, 55, 0) (14, 56, 0) (16, 201, 0) (28, 0, 0) (29, 0, 0)

1 1 :(2,231,0)(5,83,0)(7,38,0)(9,87,0)(14,245,0)(17,194,0)(29,0,0)(30,0 ,0) 12:(9,249,0)(1 1,93,0)(13,83,0)(14,20,0)(30,0,0)(31,0,0)

13:(5,39,0)(8,76,0)(11,225,0)(14,185,0)(15,1 18,0)(31,0,0)(32,0,0)

14: (5,81,0)(9,182,0)(10,248,0)(11 ,68,0)(14,23,0)(32,0,0)(33,0,0)

15: (1,183,0)(5,1 11 ,0)(11 ,230,0)(12,246,0)(14,105,0)(33,0,0)(34,0,0)

16:(5,87,0)(8,244,0)(9,183,0)(11,139,0)(14,141,0)(34,0,0)(35,0,0)

17:(5,153,0)(7,238,0)(11 ,80,0)(13,92,0)(14,75,0)(18,48,0)(35,0,0)

As another embodiment of the above encoding device:

The code rate R is 3/4, the code length Ν is 9216, the expansion ratio is 10^256, and the line weight distribution of the excessive base matrix ΒΤ is {λ16, λ14}={1/9, 8/9}, column redistribution For

{ρ9, ρ5, ρ4, ρ3, ρ2} = {1/18, 1/9, 2/9, 7/18, 2/9};

The row weight distribution of Η is {λ16, λ15, λ14}={15/144,1/144,8/9}, and the column redistribution is

{ρ9,ρ8,ρ5,ρ4,ρ3,ρ2}={35/576,1/576,1/9,2/9,7/18,2/9} ;

The check matrix Η is specifically:

0: (1,150,0)(2,223,0)(6,246,0)(8,236,0)(10,236,0)(11 ,78,0)(13,137,0)(17,48,0) (18,23 ,0)(20,195,0)(23,87,0)(25,194,0)(27,60,0)(28,0,0)

1 :(4,188,0)(8,212,0)(10,202,0)(11 ,213,0)(13,252,0)(15,150,0)(18,205,0) (20,146,0)(21,234,0 )(23,207,0)(25,15,0)(28,0,0)(29,0,0)

2:(4,243,0)(7,241,0)(9,0,0)(1 1,254,0)(13,17,0)(16,237,0)(17,254,0)(18,18,0) (21,111,0)(23,235,0)(25,25,0)(29,0,0)(30,0,0)

6:(2,247,0)(3,252,0)(7,246,0)(8,226,0)(ll,251,0)(12,251,0)(13,222,0x400) (15,182,0)(17,186,0)( 19,3,0)(22,199,0)(23,199,0)(26,199,0)(33,0,0)(34,0,0) 7:(5,250,0)(6,62,0)( 7,150,0)(10,158,0)(12,250,0)(13,90,0)(16,3,0)(19,111,0) (22,207,0)(23,39,0)(25,199,0) (34,0,0)(35,0,0)

8: (1,49,0)(5,229,0)(10,255,0)(12,254,0)(13,227,0)(15,69,0)(16,98,0)(20,70,0) (22,197,0)(23,208,0)(24, 199,0)(27, 199,0)(35,0,0).

Figure 6 is a schematic diagram of simulation of Embodiment 1 of the present invention. As can be seen from Fig. 6, the 1/2 code rate LDPC code constructed in Embodiment 1 has an SNR of about l.ldB when the BER reaches 10-4, and has excellent performance close to the theoretical limit.

The technical solution proposed by the embodiment of the present invention can construct an LDPC code with excellent performance at an arbitrary code rate. In addition, the technical solution proposed by the embodiment of the present invention also solves the storage problem of the check matrix, and effectively reduces the implementation complexity of the encoder. The LDPC code constructed by the technical solution proposed by the embodiment of the present invention can be fully compatible with the physical layer structure of the CMMB system, and can effectively improve the link margin of the system. Moreover, the technical solution proposed by the present invention also solves the problem of the degree distribution of the quasi-cyclic LDPC code and enhances the performance of the code set.

A person skilled in the art can understand that all or part of the steps carried by the method of the foregoing embodiment can be completed by a program to instruct related hardware, and the program can be stored in a computer readable storage medium. , including one or a combination of the steps of the method embodiments.

In addition, each functional unit in each embodiment of the present invention may be integrated into one processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above integrated modules can be implemented in the form of hardware or in the form of software functional modules. The integrated modules, if implemented in the form of software functional modules and sold or used as separate products, may also be stored in a computer readable storage medium.

The above-mentioned storage medium may be a read only memory, a magnetic disk or an optical disk or the like.

The above is only a preferred embodiment of the present invention, and it should be noted that those skilled in the art can also make several improvements and retouchings without departing from the principles of the present invention. It should be considered as the scope of protection of the present invention.

Claims

Rights request

A method for constructing an LDPC code check matrix, comprising the steps of: constructing a 基础-dimensional over-basic matrix BT of an LDPC code having a code rate R and a code length N, wherein MB=M/ K, NB=N/K, M = N ( 1 - R ), K is the expansion ratio of the excess basic matrix, ΚΕ Φ, Φ is the set of common factors of Μ and Ν;

Substituting the elements of the over-basic matrix ΒΤ with the matrix of ΚχΚ dimension, expanding the over-basic matrix ΒΤ into the 矩阵-dimensional over-matrix ΗΤ;

Removing at least one element "1" of at least one matrix of the ΗΤ Κ dimension of the over matrix 以获得 to obtain a test matrix Η having an optimized row weight distribution and/or column redistribution for performing LDPC Encoding and/or decoding of a code.

2. The method of constructing an LDPC code check matrix according to claim 1, wherein constructing an over-based base matrix BT that generates a LDPC code having a code rate R and a code length of N comprises the following steps:

Constructing an over-basic matrix BT of MB NB dimension, selecting the number of "1"s in each row and each column of the excessive base matrix BT, so that the row weight and column redistribution of BT satisfy a predetermined node degree distribution;

Under the premise that the row weight and the column weight satisfy the predetermined node degree distribution, the position of "1" in each row and each column in the excessive base matrix BT is selected, so that the sub-matrix of the MBxMB dimension composed of the latter MB columns of BT is full rank.

3. The method of constructing an LDPC code check matrix according to claim 2, wherein expanding the excessive base matrix BT into an MxN-dimensional over-matrix HT comprises the following steps:

Replace "0" in the excess base matrix BT with the all-zero matrix K of the KxK dimension, and replace "1" in the ΚΧΚ with the cyclic permutation matrix ΚΧΚ of the dimension, where the line number of "1" in the i And column number j satisfies j=(i+k)modk, k is the offset of the cyclic permutation matrix, and mod represents the modulo transport

"Select an offset for each cyclic permutation matrix P.

4. The method for constructing an LDPC code check matrix according to claim 2, wherein the expanding the excess base matrix BT into the MxN-dimensional check matrix HT comprises the following steps:

Replace "0" in the excess base matrix BT with the all-zero matrix K of the KxK dimension, and replace "1" in the ΒΤ with the algebraic permutation matrix ΚΧΚ of the dimension, where the line number of "1" in the i And column number j satisfies j=f(i), where f(i) is a permutation polynomial over a finite field or a ring;

Choose an offset for each algebraic permutation matrix P.

The method for constructing an LDPC code check matrix according to any one of claims 3 or 4, wherein the structure of the excessive base matrix BT or the offset of the matrix P is stored in the form of a table. Each row of the table records the position of "1" in each row of the BT or each row of the table The offset of the cyclic permutation matrix corresponding to "1" in each row of the excess base matrix BT is recorded.

The method for constructing an LDPC code check matrix according to any one of claims 3 or 4, wherein at least one element "1" of the matrix of at least one Kx K-dimensional in the over matrix HT is removed to obtain a check matrix. H includes the following steps:

For P, select r consecutive "1"s of line numbers and remove them from the excess matrix HT to obtain the check matrix H, where 0 < r ≤ K; or

For P, select r consecutive "1"s of column numbers and remove them from the excess matrix HT to obtain the check matrix H, where 0 < r ≤ K; or

For P, r "1"s are randomly selected and removed from the excess matrix HT to obtain a check matrix H, where 0 < r ≤ K.

The method for constructing an LDPC code check matrix according to claim 1, wherein the code rate R is 1/2, the code length N is 9216, and the expansion ratio K is 256. The line weight distribution of the excessive base matrix BT is {λ7, λ8, λ9, λ10}={1/18, 14/18, 1/18, 2/18}, and the column weight distribution is {ρ15, ρ5, ρ4, ρ3, Ρ2}={4/36,4/36,1/36,10/36,17/36}; the line weight distribution of Η is { λ 7, λ 8, λ 9, λ 10}={17/288,223/ 288, 1/18, 2/18}, the column weight distribution is { ρ 15, ρ 14, ρ 5, ρ 4, ρ 3, ρ 2}={7/64,1/576,1/9,1/ 36, 5/18, 17/36}.

The method for constructing an LDPC code check matrix according to claim 7, wherein the check matrix H is specifically:

0: (1, 239, 0) (4, 166, 0) (5, 247, 0) (11, 31, 0) (12, 217, 0) (14, 72, 0) (18, 192, 0) (19, 0, 0) 1: (2,251,0)(5,153,0)(11,159,0χ200)(14,48,0)(15,31,0)(19,0,0)(20,0,0)

2: (5,230,0)(6,182,0)(11,91,0)(14,62,0)(16,170,0)(20,0,0)(21,0,0)

3: (2, 255, 0) (3, 196, 0) (5, 171, 0) (7, 26, 0) (10, 11, 0) (12, 71, 0) (17, 51, 0) (21, 0, 0) (22,0,

0)

4: (4,240,0)(5,66,0)(11,0,0)(14,118,0)(17,39,0)(22,0,0)(23,0,0)

5: (2,212,0)(3,115,0)(5,93,0)(8,210,0)(9,29,0)(14,249,0)(18,39,0)(23,0,0)

(24,0,0)

6: (3,60,0)(5,46,0)(11,40,0)(13,180,0)(17,192,0)(24,0,0)(25,0,0)

7: (4,1,0)(10,247,0)(11,142,0)(14,210,0)(16,192,0)(25,0,0)(26,0,0)

8: (5,66,0)(10,208,0)(11,31,0)(14,116,0)(15,20,0)(26,0,0)(27,0,0)

9: (2,47,0)(6,8,0)(10,40,0)(11,219,0)(17,148,0)(27,0,0)(28,0,0)

10:(5,248,0)(6,255,0)(11,55,0)(14,56,0)(16,201,0)(28,0,0)(29,0,0)

11:(2,231,0)(5,83,0)(7,38,0)(9,87,0)(14,245,0)(17,194,0)(29,0,0)(30,0, 0)

12: (9, 249, 0) (11, 93, 0) (13, 83, 0) (14, 20, 0) (30, 0, 0) (31, 0, 0)

13:(5,39,0)(8,76,0)(11,225,0)(14,185,0)(15,118,0)(31,0,0)(32,0,0)

14: (5,81,0)(9,182,0)(10,248,0)(11,68,0)(14,23,0)(32,0,0)(33,0,0) 15: (1,183,0)(5,111,0)(11,230,0)(12,246,0)(14,105,0)(33,0,0)(34,0,0)

16:(5,87,0)(8,244,0)(9,183,0)(11,139,0)(14,141,0)(34,0,0)(35,0,0)

17: (5, 153, 0) (7, 238, 0) (11, 80, 0) (13, 92, 0) (14, 75, 0) (18, 48, 0) (35, 0, 0);

The ternary group (col, shift, adj(16)) is represented by the cyclic permutation matrix P of the row col column with the offset being shifted.

The method for constructing an LDPC code check matrix according to claim 1, wherein the code rate R is 3/4, the code length N is 9216, and the expansion ratio K is 256. The line weight distribution of the excessive base matrix BT is {λ16, λ14}={1/9,8/9}, and the column weight distribution is {ρ9, ρ5, ρ4, ρ3, ρ2}={1/18, 1/9, 2/9, 7/18, 2/9};

{ρ9,ρ8,ρ5,ρ4,ρ3,ρ2}={35/576,1/576,1/9,2/9,7/18,2/9}„

The method for constructing an LDPC code check matrix according to claim 9, wherein the check matrix H is specifically:

0: (1,150,0)(2,223,0)(6,246,0)(8,236,0)(10,236,0)(11,78,0)(13,137,0)(17,48,0) (18,23 ,0)(20,195,0)(23,87,0)(25,194,0)(27,60,0)(28,0,0)

1 :(4,188,0)(8,212,0)(10,202,0)(11,213,0)(13,252,0)(15,150,0)(18,205,0)

(20,146,0)(21,234,0)(23,207,0)(25,15,0)(28,0,0)(29,0,0)

2:(4,243,0)(7,241,0)(9,0,0)(11,254,0)(13,17,0)(16,237,0)(17,254,0)(18,18,0)

(21,111,0)(23,235,0)(25,25,0)(29,0,0)(30,0,0)

3:(2,137,0)(5,243,0)(9,255,0)(11,255,0)(13,210,0)(14,6,0)(18,162,0)(19,243,0)

(21,119,0)(23,4,0)(26,5,0)(30,0,0)(31,0,0)

6:(2,247,0)(3,252,0)(7,246,0)(8,226,0)(l l,251,0)(12,251,0)(13,222,0x400)

(15,182,0)(17,186,0)(19,3,0)(22,199,0)(23,199,0)(26,199,0)(33,0,0)(34,0,0)

7: (5,250,0)(6,62,0)(7,150,0)(10,158,0)(12,250,0)(13,90,0)(16,3,0)(19,111,0)

(22,207,0)(23,39,0)(25,199,0)(34,0,0)(35,0,0)

8: (1,49,0)(5,229,0)(10,255,0)(12,254,0)(13,227,0)(15,69,0)(16,98,0)(20,70,0)

(22,197,0)(23,208,0)(24,199,0)(27,199,0)(35,0,0);

11. An apparatus for constructing an LDPC code check matrix, comprising: an excessive base matrix construction unit, an excessive matrix expansion unit, and a check matrix generation unit, wherein: An over-basic matrix construction unit for constructing an over-basic matrix BT of an MBxNB dimension of an LDPC code having a code rate R and a code length N, where MB=M/K, NB=N/K, M=N (1) - R ), K is the expansion ratio of the excess basic matrix, ΚΕ Φ, Φ is the set of common factors of Μ and Ν;

An over-matrix expansion unit for replacing elements in the excess base matrix ΒΤ with a matrix of dimensions, and expanding the excessive base matrix ΒΤ into an excessive matrix of ΜχΝ dimensions;

a check matrix generating unit for removing at least one element "1" of the matrix of at least one ΚX Κ dimension of the over matrix ΗΤ to obtain a check matrix Η having an optimized row redistribution and/or column Redistribution, used to encode and/or decode LDPC codes.

12. The apparatus for constructing an LDPC code check matrix according to claim 11, wherein the excessive base matrix construction unit is configured to construct an excessive base matrix BT of MB NB dimensions, and select each row of the excessive base matrix BT and The number of "1"s in each column is such that the row weight and the column weight distribution of the BT satisfy the predetermined node degree distribution; and each row in the excessive base matrix BT is selected on the premise that the row weight and the column weight satisfy the predetermined node degree distribution. And the position of "1" in each column, so that the sub-matrix of the MBxMB dimension composed of the last MB column of BT is full rank.

The apparatus for constructing an LDPC code check matrix according to claim 12, wherein said excessive matrix expansion unit is configured to use "0" in the excess base matrix BT with an all-zero matrix of KxK dimensions ΖReplace, replace "1" in ΒΤ with the cyclic permutation matrix ΚχΚ of ΚχΚ dimension, where the line number i and column number j of "1" in Ρ satisfy j=(i+k) modK, k is a cyclic permutation matrix The offset, mod represents the modulo operation; and is used to select an offset for each cyclic permutation matrix P.

The apparatus for constructing an LDPC code check matrix according to claim 12, wherein the excessive matrix expansion unit is configured to use "0" in the excess base matrix BT for the all-zero matrix of the dimension ΖReplace, replace "1" in ΒΤ with the algebraic permutation matrix ΚχΚ of ΚχΚ, where "the row number i and the column number j of Ρ satisfy j=f(i), where f(i) is a finite field or a permutation polynomial over the ring; and an offset is selected for each algebraic permutation matrix P.

15. An encoding method for an LDPC code, comprising the steps of: dividing a check matrix H into two sub-matrices H=[HmHp], wherein Hm is a sub-matrix of Mx(NM) dimensions, and Hp is an MxM dimension. Submatrices, Hp-1 and Hp-1Hm are calculated, and the check matrix H is obtained by:

Configured to generate a code rate R, the code length N of the LDPC code Μ _{_Β} χΝ _Β dimension over the base matrix _Β τ, where _{M B = M / K, N} B = N / K, M = N (1 - R ), K is the expansion ratio of the excess basic matrix, ΚΕ Φ, Φ is the set of common factors of Μ and Ν;

Alternatively excessive base matrix with Κ χ Κ Beta-dimensional matrix of elements _[tau], the excessive expansion of the base matrix Β _τ ΜχΝ excessive dimensional matrix Η _τ; At least one element of the matrix is removed over at least a KXK _Η τ matrix dimension "1" to obtain a check matrix H;

Calculating the check sequence pΙm(Hp-1 Hm)T of the Ι χΜ dimension according to the input information sequence m of the χ(Ν-M) dimension;

The LDPC code encoding method according to claim 15, wherein constructing an over-basic matrix BT of the LDPC code of the LDPC code having a code rate R and a code length of N comprises the following steps:

Constructing an over-basic matrix BT of MB NB dimensions, selecting the number of "one row and each column of the excessive base matrix BT" such that the row weight and the column redistribution of the BT satisfy a predetermined node degree distribution;

The LDPC code encoding method according to claim 16, wherein the expanding the excessive base matrix BT into the 过度-dimensional over-matrix HT comprises the following steps:

Replace "0" in the excess base matrix BT with the all-zero matrix ΚχΚ of the dimension, and replace "1" in the ΚΧΚ with the cyclic permutation matrix ΚΧΚ of the dimension, where the line number of "1" in the i And column number j satisfies j=(i+k) modK, k is the offset of the cyclic permutation matrix, and mod represents the modulo operation;

Select an offset for each cyclic permutation matrix P.

18. The method of encoding an LDPC code according to claim 16, wherein the expanding the excess base matrix BT to the parity check matrix HT comprises the following steps:

Replace "0" in the excess base matrix BT with the all-zero matrix ΚχΚ of the dimension, and replace "1" in the ΚχΚ with the algebraic permutation matrix ΚχΚ of the dimension, where the line number of "1" in the i And the column number j satisfies j=f(i) , where f(i) is a permutation polynomial over a finite field or a ring;

Choose an offset for each algebraic permutation matrix p.

The LDPC code encoding method according to claim 15, wherein the code rate R is 1/2, the code length N is 9216, and the expansion ratio K is 256, the excessive basic matrix The line weight distribution of BT is {λ7, λ8, λ9, λ10}={ 1/18, 14/18, 1/18, 2/18}, and the column weight distribution is {ρ15, ρ5, ρ4, ρ3, ρ2}= {4/36,4/36,1/36,10/36,17/36}; 行's row weight distribution is { λ 7, λ 8, λ 9, λ 10}={ 17/288,223/288, 1 /18,2/18} , the column weight distribution is { ρ 15, ρ 14, ρ 5, ρ 4, ρ 3, ρ 2} = {7/64,1/576,1/9,1/36,5 /18,17/36}.

The LDPC code encoding method according to claim 19, wherein the check matrix H is specifically: 0: (1,239,0)(4,166,0)(5,247,0)(11,31,0)(12,217,0)(14,72,0)(18,192,0)(19,0,0) 1 : (2,251,0)(5,153,0)(11,159,0χ200)(14,48,0)(15,31,0)(19,0,0)(20,0,0)

2: (5,230,0)(6,182,0)(11,91,0)(14,62,0)(16,170,0)(20,0,0)(21,0,0)

3: (2, 255, 0) (3, 196, 0) (5, 171, 0) (7, 26, 0) (10, 11, 0) (12, 71, 0) (17, 51, 0) (21, 0, 0) (22,0,0)

4: (4,240,0)(5,66,0)(11,0,0)(14,118,0)(17,39,0)(22,0,0)(23,0,0)

5: (2,212,0)(3,115,0)(5,93,0)(8,210,0)(9,29,0)(14,249,0)(18,39,0)(23,0,0)

(24,0,0)

6: (3,60,0)(5,46,0)(11,40,0)(13,180,0)(17,192,0)(24,0,0)(25,0,0)

7: (4,1,0)(10,247,0)(11,142,0)(14,210,0)(16,192,0)(25,0,0)(26,0,0)

8: (5,66,0)(10,208,0)(11,31,0)(14,116,0)(15,20,0)(26,0,0)(27,0,0)

9: (2,47,0)(6,8,0)(10,40,0)(11,219,0)(17,148,0)(27,0,0)(28,0,0)

10:(5,248,0)(6,255,0)(11,55,0)(14,56,0)(16,201,0)(28,0,0)(29,0,0)

11 :(2,231,0)(5,83,0)(7,38,0)(9,87,0)(14,245,0)(17,194,0)(29,0,0)(30,0, 0) 12: (9, 249, 0) (11, 93, 0) (13, 83, 0) (14, 20, 0) (30, 0, 0) (31, 0, 0)

13:(5,39,0)(8,76,0)(11,225,0)(14,185,0)(15,118,0)(31,0,0)(32,0,0)

14: (5,81,0)(9,182,0)(10,248,0)(11,68,0)(14,23,0)(32,0,0)(33,0,0)

15: (1,183,0)(5,111,0)(11,230,0)(12,246,0)(14,105,0)(33,0,0)(34,0,0)

16:(5,87,0)(8,244,0)(9,183,0)(11,139,0)(14,141,0)(34,0,0)(35,0,0)

The method for constructing an LDPC code check matrix according to claim 15, wherein the code rate R is 3/4, the code length N is 9216, and the expansion ratio K is 256. The line weight distribution of the excessive base matrix BT is {λ16, λ14}={1/9,8/9}, and the column weight distribution is {ρ9, ρ5, ρ4, ρ3, ρ2} = {1/18, 1/9, 2/9,7/18,2/9} ;

{λ16, λ15, λ14}={15/144,1/144,8/9} , the column redistribution is

{ρ9,ρ8,ρ5,ρ4,ρ3,ρ2}={35/576,1/576,1/9,2/9,7/18,2/9}„

The method for constructing an LDPC code check matrix according to claim 21, wherein the check matrix H is specifically:

1 :(4,188,0)(8,212,0)(10,202,0)(11,213,0)(13,252,0)(15,150,0)(18,205,0) (20,146,0)(21,234,0)(23,207, 0)(25,15,0)(28,0,0)(29,0,0)

2:(4,243,0)(7,241,0)(9,0,0)(11,254,0)(13,17,0)(16,237,0)(17,254,0)(18,18,0) (21,1 11,0)(23,235,0)(25,25,0)(29,0,0)(30,0,0)

3 :(2,137,0)(5,243,0)(9,255,0)(11,255,0)(13,210,0)(14,6,0)(18,162,0)(19,243,0) (21,1 19, 0)(23,4,0)(26,5,0)(30,0,0)(31,0,0)

4: (4, 141, 0) (7, 252, 0) (9, 70, 0) (13, 163, 0) (14, 4, 0) (15, 78, 0) (17, 242, 0) (19, 106, 0) (23 ,12,0)(24,212,0)(26,20,0)(31 ,0,0)(32,0,0)

5: (3, 225, 0) (6, 109, 0) (8, 154, 0) (13, 128, 0) (14, 244, 0) (15, 170, 0) (19, 148, 0) (20, 3, 0) (23, 85, 0 )(24,183,0)(27,21 1,0)(32,0,0)(33,0,0)

6:(2,247,0)(3,252,0)(7,246,0)(8,226,0)(ll,251,0)(12,251,0)(13,222,0x400) (15,182,0)(17,186,0)( 19,3,0)(22,199,0)(23,199,0)(26,199,0)(33,0,0)(34,0,0) 7:(5,250,0)(6,62,0)( 7,150,0)(10,158,0)(12,250,0)(13,90,0)(16,3,0)(19,111 ,0) (22,207,0)(23,39,0)(25,199,0) (34,0,0)(35,0,0)

8: (1,49,0)(5,229,0)(10,255,0)(12,254,0)(13,227,0)(15,69,0)(16,98,0)(20,70,0) (22,197,0)(23,208,0)(24, 199,0)(27, 199,0)(35,0,0);