CN103427847A - Method for constructing LDPC codes - Google Patents

Abstract

The invention discloses a method for constructing LDPC codes. The method comprises the following steps that: step 1, the size of a check matrix of the LDPC codes is set, specifically, the number of lines, the number of columns and the size of circulatory sub blocks of the check matrix are set; step 2, according to the number of the lines, the number of the columns and the size of the circulatory sub blocks, the number of the circulatory sub blocks contained in the check matrix is calculated, and optimal line-column distribution is searched, and the optimal line-column distribution uniquely determines the column degree value of each circulatory sub block; a code table of the LDPC codes is set, such that each circulatory sub block is corresponding to one line in the code table, and the number of the figures of the corresponding line is equal to the column degree value of the circulatory sub block; and a step 3, values of the figures in the code table are determined. Codes constructed by using the method of the invention are irregular codes; with the design of column weight distribution and a short-cycle elimination algorithm adopted, the performance of the codes is close to Shannon limit; with double diagonal form-degree two-node design adopted, the implementation of an encoder can be simplified; and considerations are given to the regularization of line weight, such that the error floor of the codes can be decreased.

Description

The code construction method of LDPC code

Technical field

The present invention relates to a kind of code construction method, specifically, it is related to a kind of code construction method of LDPC code.

Background technology

LDPC code was proposed in his thesis for the doctorate first in 1963 by Gallager, Gallager also proposed the probability decoding algorithm of LDPC code simultaneously, but it is due to that probability iterative decoding calculates excessively complexity, in view of state-of-art at that time is difficult to, therefore LDPC code never hears of since then soon on the circle of communication at that time.Afterwards, except Tanner eighties of last century visualize the eighties iterative decoding is described with bipartite graph in addition to, almost no scholar had more concerns to LDPC code again.

And in 1993, the proposition of Turbo code then caused people after 45 years, see first it is a kind of can approach Shannon limit encoding scheme.So far people just start to notice the premium properties that iterative decoding possesses, at the same time, and the iteration theory based on bipartite graph (Tanner figures) also achieves very big breakthrough：Error correction procedure is construed to the process that mistake is gradually decreased by Spielman [11], and demonstrate the encoding and decoding algorithm based on bipartite graph there is linear complexity, there is scholar to propose the condition and method for scheming bipartite graph of the generation with certain error correcting capability using Expander again on this basis, Kschischang et al. establishes factor graph (Factor Graph) theory again afterwards, has further deepened the graph theory basis based on LDPC iterative decodings；On these Research foundations, Wiber then proposes the LDPC iterative decoding algorithms based on figure.These all development foundations so that in nineteen ninety-five, Mackay and Neal are found that LDPC code has the performance for approaching shannon limit as Turbo code, so as to trigger the upsurge to LDPC code research.

Due to LDPC code than Turbo code technically, especially in complexity it is more advantageous, be suitable for system in future high speed data transfer and high performance requirement, therefore be used widely.Had at present using the communication system of LDPC code word：European second generation digital broadcast television transmission standard DVB2 series；IEEE 802.11n WLAN standards；IEEE802.11e wireless wide area network standards；China Digital TV ground transmission standard (DTTB), and North America CCSDS near-earth, deep space communication system etc..

But because LDPC development is later so that it narrowly misses with 3G (Third Generation) Moblie, but in following 4G mobile communication standards IEEE 802.16m and North America new-generation digital television ground standard, LDPC will be strong competitor.

At present, LDPC theoretical foundation is really gradually perfect, and the research to this kind of code word is gradually transferred to the research of theoretical set application demand from pure theory, such as how further to improve the error correcting capability of decoding algorithm with lower hardware implementation complexity；Such as how in the case of keeping original system hardware spending not become, application demand that acquisition LDPC is adaptive, multi code Rate of Chinese character is transmitted etc.；Such as how under Gbps ultrahigh speed transmission demand, LDPC code word is designed so that error floor can be reduced to 10-12 or the 10-15 order of magnitude；Such as in the case of given code length code check, sub-block size, a set of optimal, no Fourth Ring of degree distribution, structure are designed since how developing mathematical generation method that is a set of easy and being easy to description and tries one's best random and encodes simple code word generating platform.

The content of the invention

The purpose of the present invention aims to provide a kind of code construction method of LDPC code, to solve various deficiencies present in prior art.

According to above-mentioned purpose, implement the code construction method of the LDPC code of the present invention, comprise the following steps：Step one, the size of the check matrix of setting LDPC code, includes number of lines, column number, the size for circulating sub-block of setting check matrix.Step 2, according to number of lines, column number and the size for circulating sub-block, calculates the number for the circulation sub-block that check matrix is included, the optimal ranks degree distribution of search one, ranks degree distribution has uniquely determined the row angle value of each circulation sub-block；The code table of LDPC code is set, makes corresponding a line in each circulation sub-block correspondence code table, and the digital number of corresponding a line is equal with the row angle value for circulating sub-block.Step 3, determines the digital value of each in code table.

According to above-mentioned principal character, the method for the optimal ranks degree distribution of search one is in step 2：Set the selectable value of row degree；For each circulation sub-block, a row angle value is selected from selectable value, different circulation sub-blocks can select identical row angle value；The row angle value of each circulation sub-block selection constitutes a row degree distribution, obtains multiple row degree distributions, and each row degree distribution can correspond to multiple row degree distributions again；For the distribution of each row degree, the row degree of distribution rule, the ranks degree that partners distribution are only selected；In each pair of ranks degree distribution, it is distributed with the ranks degree of EXIT Chart algorithms or density evolution theory search with minimum decoding gate limit value, the ranks Degree distributions have answered the digital number of each row in code table.

According to above-mentioned principal character, check matrix is the matrix of m rows × n row, and is divided into the information bit part of m rows × (n-m) row and the odd even redundant bit part of m rows × m row.Information bit part includes multiple circulation sub-blocks, and circulation sub-block is the matrix of m rows × q row, circulates the number of sub-blockThe cycle that q circulates for the circular matrix block of circulation sub-block.

According to above-mentioned principal character, the number of the circular matrix block of each circulation sub-block

And also meet

And

Wherein

For the maximum column angle value of check matrix.

According to above-mentioned principal character, set information bit section isCirculation sub-block is H_l, wherein l=1,2 ..., L, and its row weight is

So that the number of code table l line number words is

And

Individual numerical value is circulation sub-block H_lThe first row of submatrix

Individual 1 position.

According to above-mentioned principal character, circulation sub-block H_lIn first row

The collection of individual 1 position is combined into $A=\{a_i^l,i=\mathrm{1,2}\·\·\·d_v^l\},$ Wherein $a_i^l=x_i^l\·Q+y_i^l,$ $x_i^l\∈\{\mathrm{1,1},\·\·\·,q-1\},$ $y_i^l\∈\{\mathrm{1,1},\·\·\·,Q-1\},$

And 1 position is in remaining q-1 row

J=1,2 ..., q-1, $i=\mathrm{1,2},\·\·\·,d_v^l.$

According to above-mentioned principal character, randomly chosen in { 0,1 ..., Q-1 }And meet described

Otherwise the number of middle identical value is chosen again no more than two.Randomly chosen in { 0,1 ..., q-1 }

And meet described

In it is different between each value, otherwise choose again.EachThe distance between be not equal to 1.

According to above-mentioned principal character, for different circulation sub-block H_lAnd H_kBetween, meet and work as

When, $(x_a^l-x_b^l)\mathrm{mod}q\≠(x_c^k-x_d^k)\mathrm{mod}q.$

According to above-mentioned principal character, regular row degree distribution has following form：

Wherein, the row angle value that the k and k+1 on x indexes are represented in check matrix respectively is k, k+1, and

Represent that the quantity of the row that row angle value is k in check matrix accounts for total line number m ratio and isEqually

Represent that the quantity of the row that row angle value is k+1 in check matrix accounts for total line number m ratio and is

Wherein

It is the average value of row weight, is from the average row weight in the row degree distribution of determination

Get, relation is,

For thanSmall maximum integer,

For than

Big smallest positive integral.

In order to ensure that above-mentioned row degree distribution has

Rule format, set { 0,1 ..., (ρ₁Q-1 each value in) } is repeated

It is secondary, obtain space Y₁, set { ρ₁Q ..., Q-1 } in each value repeat

It is secondary to obtain space Y₂.Every time

It is random from Y={ Y₁, Y₂Take a value, value after, then corresponding value is just in Y={ Y₁, Y₂Middle reduction one.Wherein

For average row weight.

According to above-mentioned principal character, invention additionally discloses the code word that a variety of LDPC code generation methods according to the present invention are generated.

Technical scheme is employed, the IRA codes similar to DVBT2 structures can be generated, and with the thresholding and performance more superior than DVBT2 code word.The LDPC code word of the present invention is irregular code word, the design of column weight distribution, the elimination algorithm of becate cause codeword performance close to shannon limit, the design of double nodes of diagonal form degree 2 simplifies the realization of encoder, and the regularization of row weight considers can be with the realization of simplified decoding device and the error floor of reduction code word.On the whole, the low Partly parallel decoding device of complexity can be achieved using q × q submatrix block as decoding unit in code word of the invention.

Brief description of the drawings

In the present invention, identical reference represents identical feature all the time, wherein：

Fig. 1 is the flow chart of LDPC code generation method of the present invention.

Embodiment

Technical scheme is further illustrated with reference to the accompanying drawings and examples.

Target of the present invention is to determine the code table of LDPC code, as a rule, and code length, code check are given, i.e. the size of check matrix H m × n is given, other factors, such as circulates the size q etc. of sub-block, can all be needed and determined by design.As shown in figure 1, realizing the generation of LDPC code of the present invention below by three key steps.

The first step：The size of the check matrix of LDPC code is set, includes number of lines, the columns of setting check matrix Mesh, the size for circulating sub-block.

Specifically, for the check matrix of LDPC code, set its form asIn check matrix H_m×nIn,

The corresponding part of expression information bit, and P_m×mFor the part corresponding to odd even redundant bit, in the present invention, P_m×mFor bidiagonal matrix, i.e.,

Give above-mentioned check matrix H_m×nParameter m, n, q, wherein m represents check matrix H_m×nNumber of lines, n represents check matrix H_m×nColumn number, m × q represents check matrix H_m×nThe size of middle circulation sub-block, has in addition

The P that can be now determined_m×m.Q, the Q generally selected meets following relation：

$q>d_v^{\max }(d_v^{\max }-1)---\left(1\right)$

$Q>d_v^{\max }---\left(2\right)$

Wherein

Represent H_m×nMaximum column angle value.

Second step：According to number of lines, column number and the size for circulating sub-block, circulation that check matrix is included is calculated The number of block, the optimal ranks degree distribution of search one, ranks degree distribution has uniquely determined each circulation sub-block Row angle value；The code table of LDPC code is set, makes corresponding a line in each circulation sub-block correspondence code table, and accordingly The digital number of a line is equal with the row angle value for circulating sub-block.

Specifically, in the check matrix H of above-mentioned LDPC code_m×nZoned format in, i.e., information bit part by it is multiple circulation sub-blocks constitute, its matrix form is

Each H_lReferred to as circulate sub-block.

Next it needs to be determined that part corresponding to information bit, i.e.,Wherein

Each circulation sub-block H_lSize be m rows q row, i.e. m × q, and circulate sub-block H_lThe row angle value of each internal row is identical (row degree is row weight, and representing matrix one includes the number of non-' 0 ' numerical value in arranging).And to determine

It is exactly it needs to be determined that the code table of L rows；Determine that the code table is then mainly concerned with two aspects：

(1) each H in code table_lThe determination of the digital number of corresponding row；

(2) the digital determination of each in code table；

For (1), the distribution of row degree determines that can use external information transfer figure (EXIT-Chart) principle scans for, and obtains optimal ranks degree distribution.The generation method of the present invention uses external information transfer figure (EXIT-Chart) principle to determine that ranks degree is distributed, and is distributed with searching out an optimal degree, the theoretical threshold value Eb/No corresponding to the Optimal Distribution is minimum, and it is concretely comprised the following steps：

1) selectable value of row degree, d are determined₁, d₂..., d_K, all values are all higher than 2.

2) basis

In value L, select it is each circulation sub-block selected by d_k∈{d₁, d₂..., d_K, different circulation sub-blocks can select identical d_kValue, thus it is shared

Plant different row degree distributed combinations.

3) to any row degree part, a variety of possible row degree distributions are corresponded to, effective utilization of resource and the possible error floor of elimination in being realized for hardware, when searching for the distribution of most goodness ranks degree with external information transfer figure (EXIT-Chart), those are eliminated in advance is distributed irregular row degree, only consider the row degree of rule degree distribution, i.e., be distributed for any one row degree, its corresponding row degree distribution has following unique form：

Wherein

It is the average value of row weight, is from the average row weight in the row degree distribution of determinationGet, relation is,

Wherein,For than

Big smallest positive integral,

For than

Small maximum integer.Row degree (or cry row weight) value that k and k+1 on x indexes represent in check matrix respectively is K, K+1, and

Represent that the quantity of the row that row degree (row weight) value is k in H-matrix accounts for total line number m ratio and is

Equally

Represent that the quantity of the row that row degree (row weight) value is K+1 in H-matrix accounts for total line number m ratio and is

4) according to 2), 3) understanding, have

Ranks degree is distributed, with external information transfer figure (EXIT Chart) principle analysis

Ranks degree is distributed, each threshold value to distribution is calculated respectively, its principle is to give the distribution of certain ranks degree, searches for Eb/No so that two transfer curves fitting in external information figure, then the Eb/No is the threshold value of ranks degree distribution.Search out the ranks degree with minimum Eb/No threshold values to be distributed, as our optimal selection, i.e., be distributed according to the row degree of the optimal selection, obtain each H_lCorresponding code table l line number word numbers.

In, for each H_lCorresponding q row, make H_l(wherein H_lSize be m rows q row) row weight be

Then the number of code table l line number words isAnd be somebody's turn to do

Individual numerical value is H_lThe first row of submatrix

Individual ' 1 ' position.

Make H_lFirst row in

The collection of individual ' 1 ' position is combined intoWherein：

$a_i^l=x_i^l*Q+y_i^l,x_i^l\∈\{\mathrm{0,1},...q-1\},y_i^l\∈\{\mathrm{0,1},...,Q-1\},i=\mathrm{1,2},...,d_v^l---\left(3\right)$

And H_l' 1 ' position is obtained by following relation in remaining q-1 row：

$a_{j,i}^l=(j*Q+a_i^l)\mathrm{mod}m,j=\mathrm{1,2},...,q-1,i=\mathrm{1,2},...,d_v^l---\left(4\right)$

Using (3), (4) formula as above, as long as obtaining all H_l' 1 ' position of middle first row, you can all to obtainIn ' 1 ' position.

So only needing to determine

Value, that is, determine (3) formula inTo value, wherein $x_i^l\∈\{\mathrm{0,1},...q-1\},$ $y_i^l\∈\{\mathrm{0,1},...Q-1\}.$

3rd step：The digital value of each in code table is determined, using following create-rule：

For (2) in above-mentioned second step, each digital determination in code table.

For given H_l：

A. randomly chosen in { 0,1 ..., Q-1 }

And makeValue selection meet exist

The number of the value of middle identical value is no more than two.

B. correspondingly,

Value be also to be randomly selected in { 0,1 ..., q-1 }, it is and different between each value, i.e., randomly chosen in { 0,1 ..., q-1 } $\{x_1^l,x_2^l,\·\·\·,x_{d_l^v}^l\},$ And meet $\{x_1^l,x_2^l,\·\·\·,x_{d_l^v}^l\},$ In it is different between each value, otherwise choose again.

C. each is finally met

The distance between be not equal to 1, i.e.,

In addition, above-mentioned selection condition will also meet 2 constraintss：

1) for different H_l, H_kBetween：

Meet and work as $y_a^l=y_c^k,y_b^l=y_d^k$ When, $(x_a^l-x_b^l)\mathrm{mod}q!=(x_c^k-x_d^k)\mathrm{mod}q.$

2) following rule limits y valued space：

Set { 0,1 ..., (ρ₁Q-1 each value in) } is repeated

It is secondary, obtain space Y₁；Set { ρ₁Q ..., Q-1 } in each value repeat

It is secondary to obtain space Y₂, wherein

For average row weight.It is so each

Randomly from Y={ Y₁, Y₂A value is taken, it is then corresponding after value success to be worth just in Y={ Y₁, Y₂Middle reduction one.

Finally according to above-mentioned generation method, for each H_l, i.e., for each l, a line can be generated $a_i^l,$ $i=\mathrm{1,2},...,d_v^l.$

Illustrate the code construction method according to LDPC code of the present invention below by multiple embodiments, can obtain and be not limited to following several code words：

Embodiment 1：Code word has

Code check, code length are that the 16200, size of circulation sub-block is 360, and its code table is：

Embodiment 2：Code word has

Code check, code length are that the 16200, size of circulation sub-block is 360, and its code table is：

Embodiment 3：Code word has

Code check, code length are that the 16200, size of circulation sub-block is 360, and its code table is：

Embodiment 4：Code word has

Code check, code length are that the 64800, size of circulation sub-block is 360, and its code table is：

Embodiment 5：Code word has

Code check, code length are that the 64800, size of circulation sub-block is 360, and its code table is：

Embodiment 6：Code word has

Code check, code length are that the 64800, size of circulation sub-block is 360, and its code table is：

Those of ordinary skill in the art is it should be appreciated that the specification of the above is only one or more of embodiments in numerous embodiments of the invention, and not uses limitation of the invention.It is any for technical schemes such as the equivalent change of embodiment described above, modification and equivalent substitutes, as long as meet the present invention spirit, will all fall in the range of claims of the present invention is protected.

Claims (16)

1. a kind of code construction method of LDPC code, it is characterized in that, comprise the following steps：

Step one, the size of the check matrix of setting LDPC code, includes number of lines, column number, the size for circulating sub-block of the setting check matrix；

Step 2, according to the number of lines, column number and the size for circulating sub-block, calculates the number for the circulation sub-block that the check matrix is included, the optimal ranks degree distribution of search one, ranks degree distribution has uniquely determined the row angle value of each circulation sub-block；The code table of LDPC code is set, makes corresponding a line in each circulation sub-block correspondence code table, and the digital number of corresponding a line is equal with the row angle value of the circulation sub-block；

Step 3, determines the digital value of each in the code table.

2. the method as described in claim 1, it is characterized in that, the method that an optimal ranks degree distribution is searched in the step 2 is：

Set the selectable value of row degree；

For each circulation sub-block, a row angle value is selected from the selectable value, different circulation sub-blocks can select identical row angle value；

The row angle value of each circulation sub-block selection constitutes a row degree distribution, obtains multiple row degree distributions, and each row degree distribution can correspond to multiple row degree distributions again；

For the distribution of each row degree, the row degree of distribution rule, the ranks degree that partners distribution are only selected；

In each pair of ranks degree distribution, ranks degree distribution of the search with minimum decoding gate limit value, the ranks Degree distributions have answered the digital number of each row in code table.

3. method as claimed in claim 2, it is characterized in that, the check matrix is the matrix of m rows × n row, and is divided into the information bit part of m rows × (n-m) row and the odd even redundant bit part of m rows × m row；

Described information bit section includes multiple circulation sub-blocks, and the circulation sub-block is the matrix of m rows × q row, the number of the circulation sub-block

The cycle that q circulates for the circular matrix block of the circulation sub-block.

4. method as claimed in claim 3, it is characterized in that, the number of the circular matrix block of each circulation sub-block

And also meet

And

Wherein

For the maximum column angle value of the check matrix.

5. method as claimed in claim 4, it is characterized in that, set described information bit section asThe circulation sub-block is H_l, and its row weight is

So that the number of the code table l line number words is

And it is described

Individual numerical value is the circulation sub-block H_lThe first row of submatrix

Individual 1 position.

6. method as claimed in claim 5, it is characterized in that, the circulation sub-block H_lIn first row

The collection of individual 1 position is combined into $A=\{a_i^l,i=\mathrm{1,2},\·\·\·d_v^l\},$ Wherein $a_i^l=x_i^l\·Q+y_i^l,$ $x_i^l\∈\{\mathrm{0,1},\·\·\·q-1\},$

And 1 position is in remaining q-1 row $a_{j,i}^l=(j*Q+a_i^l)\mathrm{mod}m,$ J=1,2 ..., q-1, $i=\mathrm{1,2},\·\·\·,d_v^l.$

7. method as claimed in claim 6, it is characterized in that, randomly chosen in { 0,1 ..., Q-1 } $\{y_1^l,y_2^l,\·\·\·,y_{d_l^v}^l\},$ And meet described $\{y_1^l,y_2^l,\·\·\·,y_{d_l^v}^l\},$ Otherwise the number of middle identical value is chosen again no more than two；

Randomly chosen in { 0,1 ..., q-1 }

And meet describedIn it is different between each value, otherwise choose again；

Each

The distance between be not equal to 1.

8. method as claimed in claim 7, it is characterized in that, for different circulation sub-block H_lAnd H_kBetween, meet and work as $y_a^l=y_c^k,$ When, $(x_a^l-x_b^l)\mathrm{mod}q\≠(x_c^k-x_d^k)\mathrm{mod}q.$

9. method as claimed in claim 7, it is characterized in that, the regular row degree distribution has following form：

Wherein, the row angle value that the k and k+1 on x indexes are represented in the check matrix respectively is k, k+1, and

Represent that the quantity of the row that row angle value is k in check matrix accounts for total line number m ratio and is

Equally

Represent that the quantity of the row that row angle value is k+1 in check matrix accounts for total line number m ratio and is

Wherein

It is the average value of check matrix row weight, is from the average row weight in the row degree distribution of determination

Get, relation is,

For than

Small maximum integer,

For thanBig smallest positive integral.

10. method as claimed in claim 9, it is characterized in that, set { 0,1 ..., (ρ₁Q-1 each value in) } is repeated

It is secondary, obtain space Y₁；

Set { ρ₁Q ..., Q-1 } in each value repeat

It is secondary to obtain space Y₂；

Every time

It is random from Y={ Y₁, Y₂Take a value, value after, then corresponding value is just in Y={ Y₁, Y₂Middle reduction one.

Wherein

For average row weight.

11. a kind of LDPC code word of the method as described in claim 1 generation, it is characterized in that, the code word has

Code check, code length are that the 16200, size of circulation sub-block is 360, and its code table is：

12. a kind of LDPC code word of the method as described in claim 1 generation, it is characterized in that, the code word has

Code check, code length are that the 16200, size of circulation sub-block is 360, and its code table is：

13. a kind of LDPC code word of the method as described in claim 1 generation, it is characterized in that, the code word has

Code check, code length are that the 16200, size of circulation sub-block is 360, and its code table is：

14. a kind of LDPC code word of the method as described in claim 1 generation, it is characterized in that, the code word has

Code check, code length are that the 64800, size of circulation sub-block is 360, and its code table is：

15. a kind of LDPC code word of the method as described in claim 1 generation, it is characterized in that, the code word has

Code check, code length are that the 64800, size of circulation sub-block is 360, and its code table is：

16. a kind of LDPC code word of the method as described in claim 1 generation, it is characterized in that, the code word has

Code check, code length are that the 64800, size of circulation sub-block is 360, and its code table is：

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