CN103427847B - A kind of code construction method of LDPC code - Google Patents
A kind of code construction method of LDPC code Download PDFInfo
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Abstract
Present invention is disclosed a kind of code construction method of LDPC code, comprise the following steps：Step one, sets the size of the check matrix of LDPC code, including number of lines, column number, the size of circulation sub-block for setting check matrix.Step 2, according to the size of number of lines, column number and circulation sub-block, calculates the number of the circulation sub-block that check matrix is included, and 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 circulation sub-block.Step 3, determines each digital value in code table.The code word of present invention construction 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 that the error floor of code word can be reduced.
Description
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 first by Gallager in 1963 in his thesis for the doctorate, while Gallager also proposed
The probability decoding algorithm of LDPC code, but because probability iterative decoding calculates excessively complicated, in view of state-of-art at that time
It is difficult to, therefore LDPC code never hears of since then soon on the circle of communication at that time.Afterwards, except Tanner is in eighties of last century eighties
What is visualized is described outside iterative decoding with bipartite graph, and almost no scholar had more concerns to LDPC code again.
And in 1993, the proposition of Turbo code then caused people after 45 years, one kind is seen first can approach
The encoding scheme of Shannon limits.So far people just start to notice the premium properties that iterative decoding possesses, at the same time,
Iteration theory based on bipartite graph (Tanner figures) also achieves very big breakthrough：Be construed to for error correction procedure by Spielman [11]
The process that mistake is gradually decreased, and demonstrate the encoding and decoding algorithm based on bipartite graph there is linear complexity, on this basis
There is scholar to propose condition and method using Expander figure bipartite graphs of the generation with certain error correcting capability again, afterwards
Kschischang et al. establishes the theory of factor graph (Factor Graph) again, has further deepened and has been translated based on LDPC iteration
The graph theory basis of code；On these Research foundations, Wiber then proposes the LDPC iterative decoding algorithms based on figure.It is all
These development foundations so that in nineteen ninety-five, Mackay and Neal are found that LDPC code has as Turbo code and approach shannon limit
Performance, 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 using the communication system of LDPC code word at present：Europe
Second generation digital broadcast television transmission standard DVB2 series；IEEE 802.11n WLAN standards；IEEE802.11e is wireless
Wide area network standard；China Digital TV ground transmission standard (DTTB), and North America CCSDS near-earth, deep space communication system etc.
Deng.
But because LDPC development is later so that it narrowly misses with 3G (Third Generation) Moblie, but in following 4G movements
In communication standard IEEE 802.16m and North America new-generation digital television ground standard, LDPC will be strong competitor.
At present, the theoretical foundation of LDPC is really gradually perfect, and the research to this kind of code word is gradually shifted from pure theory
To the research of theory set application demand, such as how further to improve decoding algorithm with lower hardware implementation complexity
Error correcting capability；Such as how in the case of keeping original system hardware spending not become, LDPC self adaptations, multi code Rate of Chinese character transmission are obtained
Application demand etc.；Such as how under the ultrahigh speed transmission demand of Gbps, LDPC code word is designed so that error floor can
It is reduced to 10-12Or 10-15The order of magnitude；Such as in the case of given code length code check, sub-block size, how to develop a set of
Designed since mathematical generation method that is easy and being easy to description a set of optimal, no Fourth Ring of degree distribution, structure try one's best it is random and
Encode simple code word generating platform.
The content of the invention
A kind of code construction method that the purpose of the present invention aims to provide LDPC code is each present in prior art to solve
Plant not enough.
According to above-mentioned purpose, implement the code construction method of LDPC code of the invention, comprise the following steps：Step one, if
Determine the size of the check matrix of LDPC code, including number of lines, column number, the size of circulation sub-block for setting check matrix.Step
Two, according to the size of number of lines, column number and circulation sub-block, calculate the number of the circulation sub-block that check matrix is included, search one
Individual optimal ranks degree distribution, ranks degree distribution has uniquely determined the row angle value of each circulation sub-block；Set the code of LDPC code
Table, the code table one LDPC matrix of correspondence, i-th sub-block row in the number correspondence LDPC matrixes of the i-th line number word in code table
Row degree, make corresponding a line in each circulation sub-block correspondence code table, and corresponding a line digital number and circulation sub-block
Row angle value it is equal.Step 3, determines each digital value in code table, wherein, the step of searching for optimal ranks degree and be distributed, bag
Contain：A selectable value for setting row degree is selected for each circulation sub-block；Each circulation sub-block is according to selected row angle value pair
Multiple row degree distributions should be obtained；The row degree of distribution rule, the ranks degree that partners distribution are selected for the distribution of each row degree；Base
Optimal ranks degree distribution is searched out in each pair of ranks degree distribution in decoding gate limit value.
According to above-mentioned principal character, the method that an optimal ranks degree distribution is searched in step 2 is：Setting row degree
Selectable value；For each circulation sub-block, a row angle value, different circulation sub-blocks is selected to be arranged from identical from selectable value
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 is distributed again
Can correspondence multiple row degree distribution；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, the row with minimum decoding gate limit value is searched for EXIT Chart algorithms or density evolution theory
Row degree is distributed, and 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 m rows × (n-m) row
Information bit part and the odd even redundant bit part of m rows × m row.Information bit part includes multiple circulation sub-blocks, circulation
Block is the matrix of m rows × q row, circulates the number of sub-blockQ is the cycle of the circular matrix block circulation for circulating sub-block.
According to above-mentioned principal character, the number of the circular matrix block of each circulation sub-blockAnd also meetAndWhereinIt is the maximum column angle value of check matrix.
According to above-mentioned principal character, set information bit section isCirculating sub-block is
Hl, wherein l=1,2 ..., L, and its row weight isSo that the number of code table l line number words isAndIndividual numerical value is
Circulation sub-block HlThe first row of submatrixIndividual 1 position.
According to above-mentioned principal character, circulation sub-block HlIn first rowThe collection of individual 1 position is combined intoWherein And 1 position is in remaining q-1 row
According to above-mentioned principal character, randomly chosen in { 0,1 ..., Q-1 }And meet
It is describedThe number of middle identical value is otherwise chosen again no more than two.Randomly 0,
1 ..., q-1 } middle selectionAnd meet describedIn between each value it is each not
It is identical, otherwise choose again.EachThe distance between be not equal to 1.
According to above-mentioned principal character, for different circulation sub-block HlAnd HkBetween, meet and work asWhen,
According to above-mentioned principal character, the row degree distribution of rule has following form：Wherein, the k and k+1 on x indexes represent the row degree in check matrix respectively
It is k, k+1 to be worth, andRow angle value is for the ratio that the quantity of the row of k accounts for total line number m is in representing check matrixEquallyRow angle value is for the ratio that the quantity of the row of k+1 accounts for total line number m is in representing check matrixWhereinIt is the average value of row weight, is from the average row weight in the row degree distribution for determiningGet, relation is, It is ratioSmall maximum integer,It is ratioBig smallest positive integral.
In order to ensure that above-mentioned row degree distribution hasRule format, setting
{0,1,…,(ρ1Q-1 each value in) } is repeatedIt is secondary, obtain space Y1, set { ρ1Q ..., Q-1 in each value weight
It is multipleIt is secondary to obtain space Y2.Every timeIt is random from Y={ Y1,Y2A value is taken, after value, then corresponding value is just in Y=
{Y1,Y2Middle reduction one.Wherein It is average row weight.
According to above-mentioned principal character, invention additionally discloses various codes generated according to LDPC code generation method of the invention
Word.
Technical scheme is employed, IRA yards similar to DVBT2 structures can be generated, and with than DVBT2
The more superior thresholding of code word and performance.LDPC code word of the invention is irregular code word, the design of column weight distribution, the elimination of becate
Algorithm causes that the design of codeword performance close to shannon limit, double nodes of diagonal form degree 2 simplifies the realization of encoder, the rule of row weight
Then changing consideration can be with the realization of simplified decoding device and the error floor of reduction code word.On the whole, code word of the invention is with q × q's
Submatrix block is decoding unit, is capable of achieving the low Partly parallel decoding device of complexity.
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.
Specific 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, and as a rule, code length, code check are given, i.e. check matrix Hsm×n
Size be given, other factors, such as circulate size q etc. of sub-block, all can be to be needed by design and determined.As schemed
Shown in 1, the generation of LDPC code of the present invention is realized below by three key steps.
The first step：Set the size of the check matrix of LDPC code, including the setting number of lines of check matrix, column number, follow
The size of ring block.
Specifically, for the check matrix of LDPC code, set its form asIn verification square
Battle array Hm×nIn,The corresponding part of expression information bit, and Pm×mPart corresponding to odd even redundant bit, in this hair
In bright, Pm×mIt is bidiagonal matrix, i.e.,
Give above-mentioned check matrix Hm×nParameter m, n, q, wherein m represents check matrix Hm×nNumber of lines, n represents school
Test matrix Hm×nColumn number, m × q represents check matrix Hm×nThe size of middle circulation sub-block, has in additionNow can be with
The P for being determinedm×m.Q, the Q for generally selecting meet following relation：
WhereinRepresent Hm×nMaximum column angle value.
Second step：According to the size of number of lines, column number and circulation sub-block, the circulation sub-block that check matrix is included is calculated
Number, the optimal ranks degree distribution of search one, ranks degree distribution has uniquely determined the row angle value of each circulation sub-block；Setting
The code table of LDPC code, makes corresponding a line in each circulation sub-block correspondence code table, and the digital number of corresponding a line with follow
The row angle value of ring block is equal.
Specifically, in the check matrix H of above-mentioned LDPC codem×nZoned format in, i.e. information bit part is by multiple
Circulation sub-block is constituted, and its matrix form isEach HlReferred to as circulate sub-block.
Next it needs to be determined that part corresponding to information bit, i.e.,WhereinEach circulation sub-block HlSize be m rows q row, i.e. m × q, and circulate sub-block HlThe row angle value of internal each row
Identical (row degree is row weight, and representing matrix one includes the number of non-' 0 ' numerical value in arranging).And to determineIt 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 tablelThe determination of the digital number of corresponding row；
(2) each digital determination 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
It is distributed to optimal ranks degree.Generation method of the invention uses external information transfer figure (EXIT-Chart) principle and comes true
Determine the distribution of ranks degree, be distributed with searching out an optimal degree, the theoretical threshold value Eb/No corresponding to the Optimal Distribution is minimum
Value, it is concretely comprised the following steps：
1) selectable value of row degree, d are determined1,d2,...,dK, all values are all higher than 2.
2) basisIn value L, select each circulation sub-block selected by dk∈{d1,
d2,...,dK, different circulation sub-blocks can select identical dkValue, thus it is totalPlant different row degree distributed combinations.
3) to any row degree part, a variety of possible row degree distributions, resource in being realized for hardware have been corresponded to
Possible error floor is effectively utilized and eliminated, most goodness ranks degree is being searched for external information transfer figure (EXIT-Chart)
During distribution, those irregular row degree of distribution are eliminated in advance, only consider the row degree of rule degree distribution, i.e., arranged for any one
Degree distribution, its corresponding row degree distribution has following unique form：Its
InIt is the average value of row weight, is from the average row weight in the row degree distribution for determiningGet, relation is,Its
In,It is ratioBig smallest positive integral,It is ratioSmall maximum integer.K and k+1 on x indexes represent verification respectively
Row degree (or cry row weight) value in matrix is K, K+1, andRow degree (row weight) value is the row of k in representing H-matrix
The ratio that quantity accounts for total line number m isEquallyRow degree (row weight) value is the row of K+1 in representing H-matrix
The ratio that quantity accounts for total line number m is
4) according to 2), 3) understanding, haveRanks degree is distributed, with external information transfer figure (EXIT Chart) principle
AnalysisRanks degree is distributed, each threshold value to being distributed is calculated respectively, its principle is to give the distribution of certain ranks degree, search
Eb/No so that the two transfer curves fitting in external information figure, then the Eb/No is the threshold value of ranks degree distribution.Search
Rope goes out to have the ranks degree of minimum Eb/No threshold values to be distributed, as our optimal selection, i.e., according to the optimal selection
Row degree is distributed, and obtains each HlCorresponding code table l line number word numbers.
In, for each HlCorresponding q row, make Hl(wherein HlSize
Be m rows q row) row weight beThen the number of code table l line number words isAnd be somebody's turn to doNumerical value is HlThe first row of submatrix
Individual ' 1 ' position.
Make HlFirst row inThe collection of individual ' 1 ' position is combined intoWherein：
And Hl' 1 ' position is obtained by following relation in remaining q-1 row：
Using (3), (4) formula as above, as long as obtaining all HlThe position of ' the 1 ' of middle first row, you can be owned
'sIn ' 1 ' position.
So only needing to determineValue, that is, determine (3) formula inTo value, its
In
3rd step：Each digital value in code table is determined, using following create-rule：
(2) in for above-mentioned second step, each digital determination in code table.
For the H for givingl：
A. randomly chosen in { 0,1 ..., Q-1 }And makeValue selection meet existThe 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,
Randomly chosen in { 0,1 ..., q-1 }And meetIn each
It is different between value, otherwise choose again.
C. each is finally metThe distance between be not equal to 1, i.e.,
In addition, above-mentioned selection condition will also meet 2 constraintss：
1) for different Hl,HkBetween：
Meet and work asWhen,
2) following rule limits the valued space of y：
Setting 0,1 ..., (ρ1Q-1 each value in) } is repeatedIt is secondary, obtain space Y1；Setting { ρ1Q,...,
Q-1 } in each value repeatIt is secondary to obtain space Y2, wherein It is average row weight.It is so eachWith
Machine ground is 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 Hl, i.e., for each l, a line can be generated
The code construction method according to LDPC code of the present invention is illustrated below by multiple embodiments, can be obtained
And it is not limited to following several code words：
Embodiment 1:Code word hasCode check, code length are that the 16200, size of circulation sub-block is 360, and its code table is：
Embodiment 2:Code word hasCode check, code length are that the 64800, size of circulation sub-block is 360, and its code table is：
Embodiment 3:Code word hasCode check, code length are that the 64800, size of circulation sub-block is 360, and its code table is：
Embodiment 4:Code word hasCode 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 numerous embodiments of the invention
In one or more implementation methods, and not use limitation of the invention.Any equalization for embodiment described above becomes
The technical schemes such as change, modification and equivalent substitute, as long as meeting spirit of the invention, will all fall in power of the invention
In the range of sharp claim is protected.
Claims (8)
1. a kind of interpretation method of LDPC code, it is characterized in that, comprise the following steps：
Step one, sets the size of the check matrix of LDPC code, including sets the number of lines of the check matrix, column number, follows
The size of ring block；
Step 2, according to the size of the number of lines, column number and circulation sub-block, calculates circulation that the check matrix is included
The number of block, 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 described each circulation sub-block described code table of correspondence, and corresponding one
Capable digital number is equal with the row angle value of the circulation sub-block；
Step 3, determines the value of each numeral in the code table,
Wherein, the check matrix is the matrix of m rows × n row, and be divided into m rows × (n-m) row information bit part 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, circulation
The number of blockQ is the cycle of the circular matrix block circulation of the circulation sub-block；
Set described information bit section asThe circulation sub-block is Hl, and its row weight
ForSo that the number of the code table l line number words isAnd it is describedIndividual numerical value is the circulation sub-block HlSubmatrix
First rowIndividual 1 position,
Wherein, the code word of the LDPC code is with circular matrix block as decoding unit.
2. the method for claim 1, it is characterized in that, a side for optimal ranks degree distribution is searched in the step 2
Method is：
Set the selectable value of row degree；
For each circulation sub-block, a row angle value, different circulation sub-blocks is selected to select identical from the selectable value
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 is distributed again
Can correspondence multiple row degree distribution；
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, search has the ranks degree distribution of minimum decoding gate limit value, the ranks Degree distributions
The digital number of each row in code table is answered.
3. the method for claim 1, it is characterized in that, the number of the circular matrix block of each circulation sub-block
And also meetAndWhereinIt is the maximum column angle value of the check matrix.
4. the method for claim 1, it is characterized in that, the circulation sub-block HlIn first rowThe collection of individual 1 position is combined intoWherein
And 1 position is in remaining q-1 row
5. method as claimed in claim 4, it is characterized in that, randomly chosen in { 0,1 ..., Q-1 }And meet describedThe number of middle identical value no more than two,
Otherwise choose again；
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.
6. method as claimed in claim 5, it is characterized in that, for different circulation sub-block HlAnd HkBetween, meet and work asWhen,
7. method as claimed in claim 5, it is characterized in that, the row degree distribution of the rule 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, andRepresent school
Row angle value in matrix is tested for the ratio that the quantity of the row of k accounts for total line number m isEquallyRepresent check matrix
Middle row angle value is for the quantity of the row of k+1 accounts for the ratio of total line number m, whereinIt is the average of check matrix row weight
Value, is from the average row weight in the row degree distribution for determiningGet, relation is, It is ratioSmall maximum
Integer,It is ratioBig smallest positive integral.
8. method as claimed in claim 7, it is characterized in that, set { 0,1 ..., (ρ1Q-1 each value in) } is repeated
It is secondary, obtain space Y1；
Setting { ρ1Q ..., Q-1 in each value repeatIt is secondary to obtain space Y2；
Every timeIt is random from Y={ Y1,Y2A value is taken, after value, then corresponding value is just in Y={ Y1,Y2Middle reduction one
It is individual；
Wherein It is average row weight.
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| CN102394659A (en) * | 2011-08-04 | 2012-03-28 | 中国科学院上海微系统与信息技术研究所 | Low density parity check (LDPC) code check matrix construction method and corresponding matrix multiply operation device |
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