WO2010022602A1

WO2010022602A1 - Method and apparatus for generating quasi-cyclic low-density parity-check codes and encoding

Info

Publication number: WO2010022602A1
Application number: PCT/CN2009/071489
Authority: WO
Inventors: 原进宏; 宁军; 刘玥; 王光健; 严茜; 曾雁星; 梁伟光
Original assignee: 华为技术有限公司
Priority date: 2008-08-26
Filing date: 2009-04-27
Publication date: 2010-03-04
Also published as: CN101662290A; CN101662290B

Abstract

The embodiments of present invention disclose a method and an apparatus for generating quasi-cyclic low-density parity-check (QC-LDPC) codes and encoding, which refer to the error-correction coding technical field of communication and information system. The method includes the following steps: determining a sequence of degree distribution according to the requirements of code rate and code length of LDPC codes to be designed and system requirements; configuring column weight of each column in a base matrix according to the selected sequence of degree distribution; configuring positions and values of non-zero elements of each column in the base matrix according to the column weights of the base matrix to obtain the base matrix; extending the obtained base matrix to generate a check matrix. A method for encoding by using the QC-LDPC codes is also disclosed. The methods and the apparatus provided by embodiments of present invention enable the finally obtained codeword to reduce the influence caused by cycle overlapping effectively.

Description

Method and apparatus for generating quasi-cyclic low-density parity check code and encoding The present application claims to be filed on August 26, 2008, the Chinese Patent Office, application number 200810142175. 0, the invention name is "generating quasi-cyclic LDPC code and encoding method" The priority of the Chinese Patent Application, the entire disclosure of which is incorporated herein by reference.

Technical field

The present invention relates to the field of error correction coding techniques for communication and information systems, and more particularly to a method and apparatus for generating quasi-cyclic low density parity check codes and codes.

Background technique

Low density parity check code (LDPC, low dens i ty par ty check) is a linear block code proposed by Galler in 1962. Because of the small number of "1" in its check matrix, It is called a low density parity check code. The LDPC code was re-proposed and improved by Mackay in 1996.

In addition to the LDPC code, the Tanner graph (see Figure 1) can be used to represent the LDPC code. The Tanner graph and the check matrix are directly corresponding, consisting of variable nodes, check nodes, and edges connecting them. Each check node Z i corresponds to the i-th row of the check matrix, and each variable node Xj corresponds to the j-th column of the check matrix. When the jth bit in the codeword participates in the i-th check equation, that is, the element at the position of the i-th row and the j-th column in the check matrix takes a value of 1, the check node and the variable node in FIG. Connected. For each node, the number of edges connected to it is called the degree of this node. The length of the smallest ring in the Tanner diagram is called the girth.

The LDPC code is an error correction coding technique that currently uses more excellent performance. Its main feature is to support iterative decoding, and the performance is close to the Shannon capacity limit. The LDPC code has lower decoding complexity and supports parallel decoding and the like, thereby facilitating the improvement of decoder throughput, and is a superior error correction coding scheme in the next generation high-speed data communication system.

At present, more commonly used is a quasi-cyclic LDPC code based on a cyclic shift matrix design. The check matrix H _{mx n is} as shown in Fig. 2, "is the code length, w is the number of check bits in the code word, information bits The number is k = _n — m. Where p is a cyclic shift matrix of zxz or a zero matrix. The check matrix H _mxn can be regarded as being extended by the expansion factor Z from the binary base check matrix of size, where " = ζχ" _δ , m = zm _b , z is an integer. When the binary base matrix is expanded, element 1 is replaced with a zxz right cyclic shift matrix, and element 0 is replaced with a zxz zero matrix. Each cyclic unit array in H ^ can be determined by its rightward cyclic shift amount, and the binary base check matrix information and the cyclic shift information can be integrated into a base check matrix, denoted as H _b . Replace 0 in H _b with -1, define zxz zero matrix, and replace 1 element with cyclic shift amount. H _mxn can be obtained directly from H _b by spreading factor expansion. When the quasi-cyclic LDPC code is constructed, based on the basis check matrix, the position of the cyclic shift matrix and the magnitude of the cyclic shift amount are determined to optimize the loop distribution.

In the process of implementing the present invention, the inventors have found that at least the following problems exist in the prior art: Due to the excessive constraints of the structure corresponding to the check bit portion in the existing linearly coded check matrix, the degree of the final designed code is made. The distribution deviates from the optimal degree distribution. The existing PEG (Progressive Edge Growth) algorithm for constructing quasi-cyclic LDPC codes is considered from the perspective of a single element in each column of the basic matrix, and the non-zero element position of the basic matrix is set only from the basic matrix. The perspective is considered, so this may result in a weaker performance of the code resulting from the final search.

Summary of the invention

The embodiment of the invention provides a method for constructing an effective multi-element LDPC code applied in a quasi-cyclic structure, which fully considers the problem of ring overlap in the basic matrix, so that the resulting code effectively weakens the influence of ring overlap. .

An embodiment of the present invention provides a method for generating a quasi-cyclic low-density parity check code, where the method includes:

Determining a degree distribution sequence according to the code rate and code length requirement and system requirement of the low density parity check code to be designed;

Setting the column weight of each column of the basic matrix according to the selected degree distribution sequence;

Resetting the position and value of each column of non-zero elements in the basic matrix according to the basic matrix column, To the basic matrix;

The resulting basic matrix is expanded into a check matrix.

At the same time, the embodiment of the present invention further provides a method for encoding using a quasi-cyclic low-density parity check code, where the method is:

Perform block processing on the check matrix;

If the information sequence to be encoded is S, the information sequence is S according to the block matrix result, and the coded code word X is x = [s, p ₂ , _Pl ], and the low density parity check code is used. The check equation obtains p ₂ , and _P1 is obtained by using the value of p ₂ and a special matrix sub-block using a check equation of a low-density parity check code, and the special matrix sub-block is expanded without a column weight in the obtained check matrix. A block of 1.

Naturally, an embodiment of the present invention further provides a quasi-cyclic low-density parity check code encoder, where the encoder includes:

The check matrix generating unit is configured to design a check matrix of the quasi-cyclic low-density parity check code, wherein the check matrix is expanded by the basic matrix, and the check matrix H obtained by the basic matrix expansion is used by the sub-matrix! ^ and submatrix H _p composition, the submatrix! ^ corresponding to the system information bit portion of the codeword, the sub-matrix H _p corresponds to the check bit portion of the code word, wherein the sub-matrix H _p includes a special sub-block P ^se , and the sub-block P ^{se is} expanded and the check is expanded. There are no blocks with a column weight of 1 in the matrix.

Further, an embodiment of the present invention provides an apparatus for generating a quasi-cyclic low-density parity check code, where the apparatus includes:

a degree distribution determining unit, configured to determine a degree distribution sequence according to a code rate code length requirement and a system requirement of the low density parity check code to be designed;

a column resetting unit, configured to set a column weight of each column of the basic matrix according to the selected degree distribution sequence;

a basic matrix determining unit, configured to reset a position and a value of each column of non-zero elements in the basic matrix according to the basic matrix column to obtain a basic matrix;

An extension unit for expanding the resulting base matrix into a check matrix on a binary domain or a multivariate domain. An embodiment of the present invention further provides an apparatus for encoding using a quasi-cyclic low-density parity check code, where the apparatus includes:

a check matrix processing unit for performing block processing on the check matrix;

a calculating unit, configured to perform encoding calculation on the coded information, if the information sequence to be encoded is s, and at the same time, obtain the encoded codeword X as X = [s , P ₂ , P , using low density parity check code The check equation obtains p ₂ , and the parity check matrix obtained by expanding the special matrix sub-block P ^{se is} obtained by using the value of p ₂ and a special matrix sub-block P ^se , using the check equation of the low-density parity check code. A block of 1. Method, when constructing the basic matrix, from the perspective of the check matrix obtained after the optimization is extended, setting the position and cyclic shift value of the non-zero element in each column of the basic matrix, fully taking into account the ring overlap in the basic matrix The problem. The method and apparatus provided by the embodiments of the present invention enable the finally obtained codeword to effectively weaken the influence of the ring overlap.

DRAWINGS

Figure 1 is a Tanner diagram representation of the LDPC code;

2 is a structural diagram of a check matrix of a quasi-cyclic LDPC code;

3 is a flowchart of a method for generating a quasi-cyclic LDPC code according to an embodiment of the present invention;

4 is a structural diagram of a case where the basic structure of the H matrix is a lower triangle in the embodiment;

5 is a structural diagram of a matrix in which the basic structure of the H matrix is a lower triangular matrix in the embodiment; FIG. 6 is a P ^se matrix in which the elements in the matrix have the same value when the basic structure of the H matrix is lower triangular in the embodiment; Structure diagram

7 is a structural diagram of a matrix applied in a binary domain when the basic structure of the H matrix is a lower triangle in the embodiment;

8 is a structural diagram of the case where the basic structure of the H matrix is an upper triangular form in the embodiment;

9 is a structural diagram of a matrix in which the basic structure of the H matrix is an upper triangular matrix in the embodiment; FIG. 10 is a P ^Se applied in the binary domain when the basic structure of the H matrix is the lower triangular expression in the embodiment. a structural diagram of the matrix;

Figure 11 is a diagram showing the basic structure of an H matrix in the third embodiment;

Figure 12 is a structural diagram of a matrix in an H matrix in the third embodiment;

Figure 13 is a basic structural diagram of the H matrix in the fourth embodiment;

Figure 14 is a structural diagram of a matrix in an H matrix in the fourth embodiment;

15 is a structural block diagram of a device for generating a quasi-cyclic low density parity check code;

16 is a structural block diagram of a quasi-cyclic low density parity check code encoder;

17 is a structural block diagram of an apparatus for quasi-cyclic low density parity check code encoding.

detailed description

Embodiments of the present invention are solutions to the field of error correction coding in communication and information systems. First, a basic matrix having a specific structure is proposed. The basic matrix is used for channel coding, by which the coded data is channel coded. Moreover, the basic matrix can flexibly adjust the degree distribution to adapt to the requirements of various degrees of distribution, and includes a quasi-cyclic matrix of a specific structure in the basic matrix, so as to avoid occurrence of a column weight of 1 in the parity check matrix after expansion. Then, based on the basic structure of the basic matrix, the embodiment of the present invention provides a method for generating a quasi-cyclic LDPC code with excellent performance.

As shown in FIG. 3, a flowchart of a method for generating a quasi-cyclic LDPC code according to an embodiment of the present invention is shown.

51 01. Determine the degree distribution sequence according to the code rate and code length requirements and system requirements of the low density parity check code to be designed.

The selection of the degree distribution sequence is carried out using a method of density evolution.

51 02 , Set the column weight of each column of the basic matrix according to the selected degree distribution sequence.

This embodiment prepares to generate a basic matrix, and the basic matrix is expanded by the parity matrix H from the sub-matrix! And sub-matrix H _p , the sub-matrix corresponding to the system information bit portion of the code word, the sub-matrix corresponding to the check bit portion of the code word, wherein the sub-matrix _{ρ ρ} includes a special sub-block P ^se , the sub-block P ^{After se is} expanded, there is no block with a column weight of 1 in the parity check matrix obtained by the expansion.

51 03, resetting the position and the position of each column of non-zero elements in the basic matrix according to the basic matrix column Value, get the basic matrix.

The basic matrix H _b can be obtained by setting the position and value of each column of non-zero elements in the basic matrix in the order of the basic matrix column weights from small to large (also from large to small). The criteria for setting and searching there are such that the check matrix of the resulting code is as optimal as possible in terms of minimum loop length and ring distribution.

In a specific application, for each column, select the position of the row of the first non-zero element of the column, the element should be placed in the row with the smallest row weight in all rows, if there are multiple rows with the smallest row, then random Place it in one of the rows, and then set the value of the first non-zero element in the column to a non-negative integer less than the size of the expansion factor. For other non-zero elements of the column, traversing is placed to other locations where non-zero elements are not placed, and traversing sets the value of the non-zero element to determine the position and value of the non-zero element, the determining non-zero element The position and value of the finalized matrix is maximized and the minimum number of rings is minimized, and then the position of the non-zero element is moved to another position where no non-zero elements are placed, and The method selects the optimal value corresponding to the different positions, and finally selects a position and a value that maximizes the girth value of the final expanded check matrix among all the possible positions and corresponding values. Repeat the above steps until all non-zero elements in the column are finalized. Then traverse all the possible values of the first non-zero element of the column, and then follow the steps above to set the other element positions and corresponding values. Finally, a set of positions and values of the respective elements that maximize the girth value of the final expanded check matrix are selected.

S1 04, expanding the obtained basic matrix into a check matrix.

The application expands the basic matrix into a check matrix on a binary domain or a multivariate domain as needed. The sub-matrix H _{p is} designed as a matrix having a lower triangular form, and the scheme is introduced as a first embodiment. The bottom right corner is set to a special sub-block P ^se , which is a specific cyclic array SC (Spec if ied C i rcul ant), and the structure with the lower triangle and the specific cyclic array is called an SC-A structure. Then the basic structure of the H matrix can be a lower triangle, as shown in FIG.

For the P ^se matrix in the above-mentioned middle and lower triangular cyclic LDPC SC structure, we can use one of several forms shown in FIG.

Where is the element in the q-ary field. If the coding is further simplified, we can set the moment The elements inside the array have the same value, and the structure of the P ^se matrix can be expressed as one of FIG. When 1» is a cyclic shift array, the structure of the P ^sc matrix when applied to the binary domain can be expressed as one of FIG.

The method of encoding is described below. For the lower triangular cyclic LDPC SC-A structure in Figure 4, we can use the following encoding method for encoding.

First, the check matrix is processed in the following form:

Where A is a submatrix of (Of-l)xZ)x((NM)xZ), B is an all-zero matrix of ((Ml)xZ)xZ, and T is a ((Μ-ι) _χ ζχ ( ί -ι) _χ ζ;) grouping the lower triangular matrix, C is a

A matrix of Zx((N-M)xZ;), D is a ZxZ SC matrix, and E is a matrix of Ζχ((Μ-1)χΖ;).

If it is assumed that the information sequence to be encoded is S, the codeword obtained at the same time can be expressed as _{X =} [S, P ² , _Pl ], where _ρι corresponds to H _D in H, and part, p ₂ corresponds to H in H _D , part. So according to the check equation, we can get

As ^J +Tp ₂ +Bp =0

Cs ^r +Ep [+Dp[ =0 Since B is an all-zero submatrix, there are:

As ^r + Tp [ = 0 ρ ₂ can be calculated by backward recursion of the above formula. However, the solution requires some processing. Since pj†p ₂ and s are the quantities already obtained, there are formulas:

Since D has a specific SC structure, let's take one of Figure 5? ^∞ example for analysis, other forms for the SC structure, having a similar processing method. At this time there are:

Definition w two can be written as:

It can be found from the above formula that after the value of the first element Pi is determined, other elements can be obtained by a backward recursive method.

There are two ways to get it, Method 1:

Through the above formula we can get:

So have:

Because the addition and subtraction on the q domain are the same operation,

α + βρ _λ Zl z

a

, - 1

,·=1

Z

-1

.=2 got _Pl

And there is _1+t ^ _≠ 0. In order to determine efficiently, the two products fi ^d and ή , in the above " can be calculated using the iterative method:

i=k+\ rt can be obtained based on the n and Γ - i base stones. So the computational complexity will be linear and will be three times the complexity of using backward recursion when A is known. At the same time, the above computational complexity can be reduced by further limiting the sc matrix, such as limiting the elements in sc to a form in Figure 2:

JL ^z , ^z then have:

Zl Zl two, +1 j

The second way to calculate ^ is: We can also decompose the SC matrix D into the following form:

1 E ₁

D where is a vector of (z- ¹ ), L is a lower triangular matrix of (z- ¹ )^ ² - ¹ ),

- A non-zero element, _El is a vector of (Zl)xl. If we define Piz-i Pz

Pi "' Pz-i] _? |^

So have:

The calculation process can be expressed as:

Calculate As ^r Cs ^r ; Calculate P[; using the inverse recursion method according to the formula A^ + TP^O;

Calculate Cs^Ep using the backward recursive method to calculate -B - and yy^ + w _z ); calculate ^ = (-Β,Τ 'Ε, + A ) and Φ—, time;

Based on the above results, calculate +w _z );

Use ^Ε Ρζ Ρζ +

= Backward recursive calculation P ι, ζ-ΐ.

In a second embodiment of the present invention, _{Hp is} designed as a matrix having an upper triangular form, and a structure having an upper triangular form and a specific cyclic array is referred to as an SC-B structure. Then the structure of the H matrix is as shown in FIG. For the P ^se matrix in the upper triangular cyclic LDPC structure in FIG. 8, a few shown in FIG. 9 can be used. Forms. When applied in a binary domain, the P ^SE structure can be in the form shown in FIG.

As a third embodiment of the present invention, a check matrix structure similar to the double diagonal form can be used, in which case we design H _P as a matrix with the lower double diagonal form, and we will have the lower double diagonal form The structure of the specific cyclic array is called the SC-C structure, and the structure of the H matrix is as shown in FIG. Then in the P ^SE matrix in its structure, we can use several forms as shown in Figure 12.

In a fourth embodiment of the present invention, H _{P is} designed as a matrix having an upper double diagonal form, and a structure having an upper double diagonal form and a special subarray cyclic array is referred to as an SC-D structure. Then the basic structure of the H matrix can represent the upper double diagonal form as shown in FIG.

Then, in the P ^SE matrix, several forms as shown in Fig. 14 can be used.

In the above embodiment, the sub-blocks of the sub-matrices H _P except the special sub-blocks are expanded to:

a matrix obtained by cyclically shifting the i-bits of each element of the diagonal matrix to the right, and is a diagonal matrix of diagonal L-forms,

If q>Zl, the elements on the diagonal are different from each other; if g≤Z -l , then the Ρ ¹ diagonal contains all non-zero elements in the multivariate domain, where q is the order of the multivariate domain, Expansion factor.

A fifth embodiment of the present invention further provides an apparatus for implementing the above method. As shown in FIG. 15, a device 15 for generating a quasi-cyclic low density parity check code, the device comprising:

The degree distribution determining unit 151 is configured to determine a degree distribution sequence according to a code rate code requirement and a system requirement of the low density parity check code to be designed, and the selection of the degree distribution sequence is performed by a density evolution method.

A column resetting unit 152 is configured to set a column weight of each column of the basic matrix according to the selected degree distribution sequence. The column resetting unit 152 resets the column by: the generated check matrix H is composed of a sub-matrix and a sub-matrix HP, the sub-matrix corresponding to the system information bit portion of the codeword, and the sub-matrix H _P corresponding to the code word A parity bit portion, wherein the sub-matrix H _P includes a block having a special sub-block P ^SE , and the parity check matrix obtained by expanding the sub-block P ^{se has} no column weight of 1.

a basic matrix determining unit 153 for resetting each of the basic matrices according to the basic matrix column The position and value of the non-zero element of the column gives the basic matrix.

The basic matrix determining unit 153 includes a first non-zero element processing unit for selecting a position of a row in which the first non-zero element of the column is located, and the row in which the first non-zero element is located in all rows The minimum is small, and the first non-zero element in the column is set to a non-negative integer less than the expansion factor value; other non-zero element processing units are used for other non-zero elements of the column, placed to other The position of the non-zero element is not placed, and the value of the non-zero element is set by the traversal, the position and value of the non-zero element are determined, and the position and value of the non-zero element are determined such that the final expanded check matrix Maximize the circumference value.

An extension unit 154 is for expanding the resulting base matrix into a check matrix on a binary domain or a multivariate domain.

The portion of the basic matrix obtained by the basic matrix determining unit in the application of the apparatus is expanded by the special sub-block P ^se as shown in FIG. 5.

A sixth embodiment of the present invention, as shown in FIG. 16, is a quasi-cyclic low density parity check code encoder 16, and the encoder 16 includes:

The check matrix generating unit 160 is configured to design a check matrix of the quasi-cyclic low-density parity check code, and the check matrix is expanded by the basic matrix, and the check matrix H obtained by the basic matrix expansion is used by the sub-matrix! And sub-matrix H _p , the sub-matrix corresponding to the system information bit portion of the code word, the sub-matrix Hp corresponding to the check bit portion of the code word, wherein the sub-matrix H _p includes a special sub-block P ^se , the sub-matrix The parity check matrix obtained by block expansion has no block with a column weight of 1.

The portion obtained by expanding the special sub-block in the encoder 160 is as shown in FIG.

As shown in FIG. 17, a seventh embodiment of the present invention is an apparatus 17 for encoding a quasi-cyclic low-density parity check code, and the apparatus 17 for encoding the quasi-cyclic low-density parity check code includes:

The check matrix processing unit 171 is configured to perform block processing on the check matrix, and divide the check matrix of Μ χ 一 into one ((M_l)xZX(N_)xZ;) when performing block processing on the check matrix. Submatrix

A, one ((Μ_1)χΖ)χΖ all zero matrix B, — 1) χΖ) χ((Μ-1)χΖ) grouping lower triangular matrix T, a matrix C of Zx((N_)xZ), a special sub-array P ^sc of E, E is a matrix E of Zx((M_l)xZ), where the special sub-matrix is decomposed into one with only the first element a non-zero value ^ - ¹ ) vector - a lower triangular matrix ^τ ι of (z - ¹ )^ ² - ¹ ), a non-zero element A, a vector E _lD calculation unit 172 of (z- ¹ ), which is used for The coded information is calculated and coded. If the information sequence to be coded is s, the information sequence is s encoded according to the check matrix block result, and the coded code word X can be expressed as x = [s, P ₂ , PJ, obtaining a P ₂ using a check equation of a low-density parity check code, obtaining a special matrix sub-block extension of P _l by using a value of P ₂ and a special matrix sub-block using a check equation of a low-density parity check code The resulting check matrix has no blocks with a weight of one. The calculation unit

172 calculation? And ^ method is: according to the formula ^ ^{+ 1} [= ⁰ , using the inverse recursive method to calculate P [, and then obtain P ₂ ;

Pi called Ρΐ,Ζ—i Ρζ P

w = [w _r w _z ] , W ₃ W Ά w ₂ ... w _Z 1,Z-1 [Pi Pi ^J z-\\

In the method of constructing the basic matrix, from the perspective of optimizing the expanded check matrix, the position and cyclic shift value of the non-zero elements in each column of the basic matrix are set, and the problem of overlapping the rings in the basic matrix is fully considered. The method and apparatus provided by the embodiments of the present invention enable the finally obtained codeword to effectively weaken the influence of the ring overlap.

A person skilled in the art can understand that all or part of the process of implementing the above embodiment method can be completed by a computer program to instruct related hardware, and the program can be stored in a computer readable storage medium. In execution, the flow of an embodiment of the methods as described above may be included. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited. In this regard, any person skilled in the art can easily conceive changes or substitutions within the scope of the present invention. Therefore, the scope of the invention should be determined by the scope of the appended claims.

Claims

Claim

A method for generating a quasi-cyclic low-density parity check code, the method comprising: determining a degree distribution sequence according to a code rate and a code length requirement and a system requirement of a low-density parity check code to be designed ;

Resetting the position and value of each column of non-zero elements in the basic matrix according to the basic matrix column to obtain a basic matrix;

The resulting basic matrix is expanded into a check matrix.

2. The method according to claim 1, wherein the resetting the position and the value of each non-zero element in the basic matrix according to the basic matrix column, the process of obtaining the basic matrix comprises:

For each column:

Select the position of the row in which the first non-zero element of the column is located, the first non-zero element having the smallest row in the row;

Set the first non-zero element value in the column to a non-negative integer less than the expansion factor value; for other non-zero elements of the column, traverse to other locations where non-zero elements are not placed, and traverse the settings The value of the non-zero element determines the position and value of the non-zero element, and the position and value of the non-zero element are determined such that the girth value of the final expanded check matrix is maximized and the minimum number of rings is minimized.

3. The method according to claim 1, wherein the parity matrix H obtained by the basic matrix expansion is composed of sub-matrices! And sub-matrix HP, the sub-matrix corresponding to the system information bit portion of the codeword, the sub-matrix _{Ρ Ρ} corresponding to the check bit portion of the codeword, wherein the sub-matrix H _P includes a special sub-block P ^SE , the sub-block After the P ^{SE is} expanded, there is no block with a column weight of 1 in the check matrix obtained by the expansion.

4. The method according to claim 3, wherein the special sub-block P ^{SE is} expanded to:

Among them are elements in the multivariate domain.

5. The method according to claim 3, wherein the special sub-block P is in the binary domain ^{; the} extension is:

The method according to claim 3, wherein the special sub-block P ^{se is} expanded

^d l, 2 0 - • 0 0

0 ^d 2, 2 ^d 2, 3 . • 0 0

0 d ₃ , ₃ - • 0 0

0 . : :

- 0 0 - • ^Ζ-Ι, Ζ-Ι dz-i,z

0 0 0 - • 0 d _z , _z

7. The method of claim 3, wherein the special sub-block SC is in a binary domain

After P' is expanded, it is:

8. The method according to claim 3, wherein the sub-blocks Pi of the sub-matrices _Hp except the special sub-blocks are expanded to:

Pi is a matrix obtained by cyclically shifting the i-bits of each element of the diagonal matrix to the right, and Pi is a diagonal matrix of diagonal elements, respectively.

q>Zl, the elements on the diagonal are different from each other; if g≤Z -l , then the Ρ ¹ diagonal contains all non-zero elements in the multivariate domain, where q is the order of the multivariate domain, indicating expansion factor.

9. A method of encoding using a quasi-cyclic low density parity check code, characterized in that the method Includes:

Perform block processing on the check matrix;

If the information sequence to be encoded is S, the information sequence is S according to the parity check result, and the encoded codeword X is x = [s, p ₂ , _Pl ], and the low density parity check code is used. Check equation

P ₂ , obtaining a Pi by using a value of P ₂ and a special matrix sub-block using a check equation of a low-density parity check code, wherein the special matrix sub-block is expanded without a block having a column weight of 1 in the obtained check matrix .

The method according to claim 9, wherein the block processing is performed by dividing the check matrix into: ((Ml) _x z;) x ((NM) xZ ;) submatrix A, —

((Μ_1)χΖ)χΖ's all-zero matrix B, one ((Λ/-1)χΖ)χ((Λ/-1)χΖ) grouped lower triangular matrix Τ , one

A matrix c of Zx((7V-M)xZ), a special sub-array P ^{se of} ZxZ, E is a matrix of _Zx ( _(M - _1)xZ ), where a special sub-array? Decomposed into a lx(Zl) vector B - (Z- ¹ )^ ² - ¹ ) lower triangular matrix 1\, a non-zero element D _l - (Zl)xl vector E _lD

11. The method according to claim 10, wherein the method of calculating ₁ and is: according to the formula ^{As + Tp} [ ⁼⁰ , using the inverse recursive method to calculate P [, and then obtaining p ₂ ;

According to the formula ρ _ζ +Ό _{ )

τ

^{Pl =} [Ρ ¹ · ² - ¹ ^], w = [w _r w _z ] , W _T = [MM Ρι, ζ-ι = [ PI ■ ■ ■ Pz-x

^W Z-1

TiP +

=

12. A quasi-cyclic low density parity check code encoder, wherein: the encoder comprises: a check matrix generating unit, configured to design a check matrix of a quasi-cyclic low density parity check code, the school The matrix is expanded by the basic matrix, and the parity matrix H obtained by the basic matrix expansion is composed of sub-matrices! And the sub-matrix H _p , the sub-matrix corresponding to the system information bit portion of the code word, the sub-matrix H _p corresponding to the check bit portion of the code word, wherein the sub-matrix H _p includes a special sub-block P ^se , After the sub-block is expanded, there is no block with a column weight of 1 in the parity check matrix obtained by the expansion.

The encoder according to claim 12, wherein the special sub-block P ^se in the encoder is expanded to:

:

0 0 0 0

d ₂ , ₂ d ₂ , ₂ 0 0 0

d ₂ , ₃ d ₃ , 3 ... 0

0 0

0 0 ^Z-1, Z-1

0 0 0 ^Z, Z-1 d _z , _z

14. An apparatus for generating a quasi-cyclic low density parity check code, the apparatus comprising: a degree distribution determining unit for using a code rate code length requirement of a low density parity check code to be designed System requirements, a sequence of deterministic distributions;

a column resetting unit configured to set a column weight of each column of the basic matrix according to the selected degree distribution sequence; a basic matrix determining unit configured to reset each column in the basic matrix to be non-zero according to the basic matrix column The position and value of the element, to get the basic matrix;

An extension unit for expanding the resulting base matrix into a check matrix on a binary domain or a multivariate domain.

15. The apparatus according to claim 14, wherein the basic matrix determining unit comprises: a first non-zero element processing unit for selecting a position of a row of the first non-zero element of the column, The first non-zero element is placed in the row with the smallest row weight in all rows, and the value of the first non-zero element in the column is set to a non-negative integer less than the expansion factor value;

Other non-zero element processing units for other non-zero elements of the column, and traversed to other locations where non-zero elements are not placed, and traversing the value of the non-zero element, determining the non-zero element Position and value, the determining the location and value of the non-zero element minimizes the girth value and the minimum number of rings of the final expanded check matrix.

The apparatus according to claim 14, wherein the principle of column resetting in the column resetting unit is to make the parity matrix H obtained by expanding the generated basic matrix from the sub-matrix! And sub-matrix H _p , the sub-matrix corresponding to the system information bit portion of the code word, the sub-matrix H _p corresponding to the check bit portion of the code word, wherein the sub-matrix includes a special sub-block P ^se , the sub-block After P ^{se is} expanded, there is no block with a column weight of 1 in the parity check matrix obtained by the expansion.

The device according to claim 16, wherein the part of the binary basic matrix obtained by the basic matrix determining unit that is extended by the special sub-block P ^se is:

1 0 0

1 1 0

0 1 1

0 0 0

0 0 0 or

, or

1 1 0 - - 0 0

0 1 1 - - 0 0

0 1 - - 0 0

0

0 0 - - 1 1

0 0 0 - - 0 1

18. An apparatus for encoding using a quasi-cyclic low density parity check code, the apparatus comprising:

a calculation unit, configured to perform coding for encoding the information to be encoded, and if the information sequence to be encoded is s, encode the information sequence as s according to the block matrix result, and obtain the coded code word X as X=[ s, P ₂ , PJ, obtain p ₂ using the check equation of the low density parity check code, obtain the p _l by using the check value of the low density parity check code by the value of p ₂ and a special matrix sub-block P ^se The check matrix obtained by the expansion of the special matrix sub-block has no block with a column weight of 1.

The apparatus according to claim 18, wherein the check matrix processing unit divides the check matrix of Μ χ 一 into a submatrix ^ (^^^) when performing block processing on the check matrix. – (Af-l) ZxZ's all-zero matrix B, — (Ml)Zx(Ml)Z grouping lower triangular matrix τ, a ZxKZ The special sub-matrix P ^{sc of the} matrix, E is a matrix E of sc C , a ZxZ Z^M - ¹ ) ² , where the special sub-array P' is decomposed into a vector of (z- ¹ ) B _l — (z- ¹ )^ ² - ¹ ) lower triangular matrix 1\, a non-zero element D _l — (z-^ ¹ vector E _lD

20. The apparatus of claim 18, wherein the computing unit calculates? And the method of P ₂ is: according to the formula ^ ¹ ^ ^ ⁰ , using the inverse recursive method to calculate P [, and then obtain P ₂ ;

Dj, ,