CN104052501B - The m-ary LDPC code coding method of low complex degree - Google Patents
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Abstract
The present invention is a kind of m-ary LDPC code coding method of low complex degree, belongs to communication technical field.This method simplifies the representation of codeword information confidence level using the binary representation of multi-system symbol in iteration, the calculating for being iterating through check-node every time updates the confidence level of side information, the service efficiency that variable node opposite side information is strengthened in weighting is introduced in the calculating of variable node, and codeword information and external information are calculated using binary information updating mode.Message length r of each symbol of code word of the present invention is far below the length 2 in existing methodrSide information only has a finite field symbol and its confidence level, with very low storage complexity, the calculating of variable node and check-node is mainly addition of integer and integer comparison operation, only a small amount of finite field operations and multiplying, with very low computation complexity, for the code of various code lengths and code weight can obtain good decoding performance.
Description
Technical field
The present invention relates to a kind of m-ary LDPC code coding method of low complex degree, belongs to communication technical field.
Background technology
Low-density checksum (LDPC) code is a kind of important error correcting code, and its parity matrix has sparse spy
Property, during using belief propagation (BP) algorithm, the performance of LDPC code can be close to shannon limit.There are various communication systems at present
System, such as digital satellite television (DVB-S2), fourth generation mobile communication systems (4G), GPS (GPS) etc.,
Error Control is carried out using LDPC code in its data transfer.Non-Binary LDPC Coded is obtained in that more excellent than binary system LDPC code
Performance, but do not obtain as binary system LDPC code and rapidly promote.It is simultaneous that this is primarily due to not a kind of energy at present
Turn round and look at decoding performance and calculating, the Non-Binary LDPC Coded decoding algorithm of storage complexity.
Bipartite graph of the decoding of Non-Binary LDPC Coded based on code check matrix, or it is called Tanner figures, it is shown in Fig. 1
Two branches of one LDPC code, it is made up of the side of variable node, two kinds of nodes of check-node and connection.Its decoding process is main
It is divided into 4 parts：Storage, the storage of side information, the calculating of check-node and the calculating of variable node of codeword information.It is existing
M-ary LDPC code coding method mainly has two kinds, a kind of to be based on belief propagation (BP) algorithm, and another kind is translated based on majority logic
Code (MLgD) algorithm.Both approaches have similar codeword information, it is assumed that m-ary LDPC code check battle array is finite field gf
(2r) under matrix, then the information of each code-word symbol be a length for 2rConfidence level vector, characterize the symbol and be respectively
Finite field gf (2r) under all 2rThe uncertain proposition of individual element, needs storage 2rIndividual confidence information.And based on MLgD algorithms
M-ary LDPC code coding method is with the side information simply more than the m-ary LDPC code coding method based on BP algorithm.Base
In the side information of the m-ary LDPC code coding method of BP algorithm, based on the different implementations of BP algorithm, code word can be equal to
Information vector, its length be 2r, each edge needs storage 2rThe confidence level of individual finite field elements；Can also be according to codeword information
In vector, the confidence level size of different elements, only takes the larger Partial Elements of confidence level, it is assumed that its length is nm(n in practicem＞
1), such each edge needs to store n ＞mThe value of individual finite field elements and corresponding nmThe value of individual confidence level.Based on MLgD algorithms
The side information of m-ary LDPC code coding method is only made up of that maximum element of confidence level in codeword information, and each edge is only needed
Store the value of 1 finite field elements and 1 confidence level.In Non-Binary LDPC Coded decoding, the calculating of check-node and variable section
The calculating of point is based on codeword information and side information and carries out.Based in the m-ary LDPC code coding method of BP algorithm, check-node
It is q to the computation complexity of the side information of each two input2Magnitude (orM magnitudes, for side message length is nmReality
It is existing), the computation complexity of the side information that variable node be input into each two is q magnitudes (or 2nm, for side message length is nm
Realization).Because the side information based on the m-ary LDPC code coding method of MLgD algorithms is more simple, therefore its check-node
The computation complexity of the side information being input into each two with variable node is 1, is translated based on the Non-Binary LDPC Coded of BP algorithm
The 1/q of code method2(or)。
Although storage and computation complexity based on the m-ary LDPC code coding method of MLgD algorithms are far below and are based on
The interpretation method of the Non-Binary LDPC Coded of BP algorithm, but the performance based on the m-ary LDPC code coding method of MLgD algorithms is non-
It is often relied on the row weight of LDPC check matrix.When the row weight of code relatively low (being less than 6), its performance loss is very serious, and
In bit error rate (BER) up to 10-6Left and right is likely to occur incorrect platform.Do not have a kind of Non-Binary LDPC Coded decoding side at present
Method pervasively when the LDPC code to various parameters is decoded can obtain fine before decoding performance and calculating, storage complexity
Equilibrium.
The content of the invention
The invention aims to solve the problems, such as that polynary domain LDPC code decoding complexity and performance cannot be taken into account, propose
A kind of m-ary LDPC code coding method of low complex degree.Interpretation method of the present invention is a kind of iteration based on bipartite graph
Interpretation method, this method simplify the expression side of codeword information confidence level using the binary representation of multi-system symbol in iteration
Formula, updates the confidence level of side information in the calculating for being iterating through check-node every time, and weighting is introduced in the calculating of variable node
Strengthen the service efficiency of variable node opposite side information, and codeword information and outer letter are calculated using binary information updating mode
Breath.
LDPC code interpretation method carries out decoding initialization first, and then iteration carries out following steps：Hard decision, calculating side letter
Breath, check node calculation and variable node are calculated, until successfully decoded or failure.The present invention provide low complex degree enter
LDPC code interpretation method processed, to codeword information, represents code-word symbol using binary form, during decoding, carries out
The improvement of following aspect：
1), during decoding initialization, weighted factor is set, codeword information is initialized using bit confidence coefficient；
2) confidence level of the outside verification sum on check-node and variable node connection side is converted into bit confidence coefficient vector, ginseng
Calculate with variable node；
3) codeword information and the external information of check-node that iteration updates every time is all bit confidence coefficient vector.
Interpretation method of the present invention, when carrying out variable node calculating, the information of check-node input variable node is adopted and is based on
The confidence level weighting scheme of Hamming distance obtaining, specifically：According to the outside verification on check-node and variable node connection side
And binary representation and the binary representation of code-word symbol hard decision between Hamming distance size setting weighted factor, make
The confidence level for connecting the outside verification sum on side is weighted with weighted factor.
Interpretation method of the present invention, when on side, information is calculated, side information includes the multi-system hard decision symbol of code word external information
And the confidence level of the symbol；Wherein, the confidence level of symbol is the minimum in all absolute values in the binary digit external information of code word
Value.
In interpretation method of the present invention, all codeword informations, code word external information, the confidence level of outside verification sum and verification
Node inputs to the information of variable node and is integer.
Advantages of the present invention and good effect are：
(1) in the present invention, the message length of each symbol of code word is only r, far below the code-word symbol Chief Information Officer of existing algorithm
Degree 2r；Meanwhile, its side information only has a finite field symbol and its confidence level, with very low storage complexity；
(2) calculating of variable node and check-node of the invention is mainly addition of integer and integer comparison operation, only
A small amount of finite field operations and multiplying, with very low computation complexity；
(3) present invention is insensitive for the code weight of Non-Binary LDPC Coded, for the code of various code lengths and code weight can be obtained
Good decoding performance.
Description of the drawings
Fig. 1 is that the bipartite graph of the LDPC check matrix of the row of 5 row 10 is represented；
Fig. 2 is the flow chart of the m-ary LDPC code coding method of the present invention.
Specific embodiment
Below in conjunction with accompanying drawing and embodiment, the present invention is described in further detail.
As shown in Fig. 2 for the overall flow figure of m-ary LDPC code coding method, carrying out decoding initialization first, then
Iteration is carried out：Hard decision, calculating side information, check node calculation and variable node are calculated, until successfully decoded or failure.This
The m-ary LDPC code coding method of the low complex degree of invention, adopts binary form table to the code-word symbol of codeword information
Show, during decoding, carried out the improvement of following aspect：
1) codeword information is initialized using bit confidence coefficient；
2) confidence level of the outside verification sum on check-node and variable node connection side is converted into bit confidence coefficient vector, ginseng
Calculate with variable node；
3) codeword information and the external information of check-node that iteration updates every time is all bit confidence coefficient vector.
The m-ary LDPC code coding method of the present invention is illustrated with reference to instantiation.
Assume a Non-Binary LDPC Coded by its finite field gf (2r) under size be the zero empty of the parity check matrix H of m × n
Between define, then the code word of the Non-Binary LDPC Coded be a length be n GF (2r) under vector, the codeword vector can be with one
Individual length is equivalently represented for the binary vector of nr.With c=(c1,c2,…,cn) multi-system code word is represented, use cj(1≤j≤n)
J-th symbol of code word is represented, c is usedj=(cj,1,cj,2,…,cj,r) represent j-th symbol binary representation, cj,tRepresent the
T-th binary digit of j symbol, is worth for 0 or 1.When communication system is transmitted using BPSK modulation systems, to code word two
Each bit that system is represented does following mapping：0 →+1V, 1 → -1V.Through binary system additive white Gaussian noise (BI-
AWGN) after channel, the codeword information that system is received is y=(y1,y2,...,yn), wherein yj=(yj,1,yj,2,...,yj,r)
For the log-likelihood ratio of j-th code-word symbol r bit1≤j≤n, 1≤t≤r.M-ary LDPC
Code decoder enters row decoding using y and H.Decoding process is carried out according to the following steps：
Step one, carry out decoding initialization setting.Setting weighted factor θ0,θ1,…,θr.Setting maximum iteration time Imax。
Current iteration number of times k is set to 1.
Codeword information is initialized using bit confidence coefficient, be that y is equal with quantized interval Δ and quantizing bit number ω
It is even to be quantified as the codeword information that integer is assigned to the 1st iteration.The embodiment of the present invention is as at the beginning of following quantification manner by codeword information
Beginning turns to integer：
Wherein 1≤j≤n, 1≤t≤r, ω, Δ are respectively quantizing bit number and quantized interval, and N is integer, and-(2ω-1-
1) ＜ N ＜ 2ω-1- 1, yj,tT-th binary digit of j-th code-word symbol of binary code word information y that expression system is received
Information,Superscript 1 represent current iteration number of times,Represent j-th code-word symbol, t-th binary system in the 1st iteration
Position information.
J-th code-word symbol information of the 1st iteration is obtained by formula (1)Enter
And obtain the codeword information of the 1st iteration
Step 2, the codeword information to kth time iteration carry out hard decision：
WhereinIt is the codeword information of kth time iteration, if k=1,Initialize in step one and obtain, otherwiseUpdate in five the step of upper once iteration and obtain,Represent and j-th code-word symbol of kth time iteration is entered for t-th two
Position information processedHard decision result.AssumeIt is multi-system symbolBinary representation, then
It is the hard decision result of j-th code-word symbol of code word.By multi-system hard decision vectorWith verification square
Battle array H is verified.If z(k)HT=0, then it is successfully decoded；If z(k)HT≠ 0 and k ＞ Imax, then decoding failure；Otherwise, carry out
Step 3.It 0 is exactly to judge z to judge in Fig. 2 that whether even-odd check result is(k)HTWhether it is 0, judges to exceed when iterations
Whether maximum iteration time is exactly to judge k more than Imax。
Step 3, for all 1≤j≤n, i ∈ Mj, calculate j-th variable node and believe to the side of i-th check-node
Breath, wherein, MjRepresent that the jth of check matrix H arranges the set that all nonzero element line positions are put, it is assumed that the unit of the i-th row jth row of H
Element is hi,j, then Mj={ i:1≤i≤m,hi,j≠0}。
First, calculate the code word external information of kth time iteration.If current iteration is first time iteration, i.e. k=1, then code word
External information is equal to codeword information.The binary digit external information of j-th code-word symbol of check-nodeEqual to first time iteration
J-th code-word symbol binary piece of informationSuch as formula (3)：
During kth (k >=2) secondary iteration, codeword information of the code word external information by current iterationSchool when deducting last iteration
Test the information that node inputs to variable node corresponding with the code-word symbolObtain：
Wherein, 1≤t≤r,When representing kth time iteration, for i-th check-node, j-th code-word symbol t
The external information of individual binary digit.For last iteration when i-th check-node input to it is corresponding with j-th code-word symbol
Variable node t-th binary piece of information.The corresponding variable node of j-th code-word symbol namely j-th variable node.
(3) it is required in formula and (4) formulaNumber range be limited to (- 2ω-2+1,2ω-2- 1) in the range of, when required result exceeds
During the scope, settingValue be immediate boundary value.
Then, variable node is calculated to the side information of check-node according to code word external information.Side information in this step point
For two parts, multi-system hard decision symbol of the Part I for code word external informationAndBinary representation it is every
One be all the corresponding binary digit of code word external information hard decision：
WhereinRepresentBinary representation t positions, 1≤t≤r；R of the Part II of side information for code word
The minimum of a value of individual binary digit external information absolute value, i.e.,It represents symbolConfidence level.Here, footmark j
→ i represents the side of j-th variable node of connection and i-th check-node.
Step 4, check node calculation.Firstly, for all 1≤i≤m, calculate i-th check-node verification and
NiRepresent the set that all nonzero element line positions of the i-th row of check matrix H are put, Ni={ j:1≤j≤n,hi,j≠0}。
The side of connection check-node and variable node includes two parts information：Part I be the outside verification on the side and,
Part II is the confidence level that sum is verified outside the side；Wherein, outside side, the determination method of the confidence level of verification sum is：First,
The minimum value MIN of the confidence level on all sides that acquisition is connected with check-node1With sub-minimum MIN2, what is be connected with check-node is put
The confidence level of the outside verification sum on the minimum side of reliability is MIN2, the side that residue is connected with check-node it is outside verify and put
Reliability is MIN1.Illustrated with the information on the side being connected with i-th check-node below.
Calculate the minimum of a value and sub-minimum of the confidence information on all sides being connected with i-th check-node.By side information
Confidence level minimum of a value and sub-minimum be designated as respectivelyWithAnd it is all by what is be connected with i-th check-node
In confidence level it is minimum while sequence number be designated as ji。
Then, for check-node i, 1≤i≤m, connected all side i → j, j ∈ Ni={ j:1≤j≤n,hi,j≠
0 }, calculate the side information of each edge.The side information of this step is equally divided into two parts, and Part I is that each edge is corresponding outer
Portion verify and
Part II is the confidence level that sum is verified outside the sideTried to achieve by following formula：
Here, footmark i → j represents the side of i-th check-node of connection and j-th variable node.
Step 5, variable node are calculated.The calculating of variable node is divided into two parts.
Part I, calculates the information of check-node input variable node, is weighted using the confidence level based on Hamming distance
Mode is obtaining.According to the outside verification on check-node and variable node connection side and binary representation sentenced with code-word symbol firmly
The size setting weighted factor of the Hamming distance between binary representation certainly, is verified to connecting the outside of side using weighted factor
The confidence level of sum is weighted.For all 1≤j≤n and i ∈ Mj, in calculation procedure four the outside verification of each edge information andWith codeword information hard decision result z in current iteration step 2(k)Binary representation Hamming distance, by the distance
WithRepresent；Conventional letterBe represented in binary asThen i-th check-node is defeated
Enter and to the information of t-th binary digit of j-th variable node be
Wherein, 1≤t≤r, the information will three the step of next iteration in be used for calculate code word external information.
For weighted factor, concrete value is set in step one, according to the distance for being obtainedTo determine weighted factor
Value.In addition, this step will be requiredNumber range be limited to (- 2ω-2+1,2ω-2- 1) in the range of, if required
As a result it is more than 2ω-2- 1, then willValue be taken as 2ω-2- 1, if required result is less than -2ω-2+ 1, then willValue take
For -2ω-2+1。
The Part II that variable node is calculated is the renewal of codeword information, carries out according to the following formula：
Wherein, 1≤j≤n, 1≤t≤r, the codeword information of renewal will used in next iteration the step of two in sentenced firmly
Certainly and even-odd check.From formula (10), the binary piece of information of j-th code-word symbol during+1 iteration of kth, by two parts
Summation is obtained, and the binary piece of information of j-th code-word symbol when Part I is first time iteration, Part II are to kth
During secondary iteration each check-node input to j-th variable node binary piece of information summation obtain.
In addition, required by this stepNumber range be limited to (- 2ω-1+1,2ω-1- 1) in the range of, if required knot
Fruit is more than 2ω-1- 1, then willValue be taken as 2ω-1- 1, if required result is less than -2ω-1+ 1, then willValue be taken as -2ω-1+1。
Step 6, enter next iteration, i.e. make k=k+1, re-execute step 2.
When decoding successfully decoded or failure in step 2, decoding terminates.
Claims (6)
1. a kind of m-ary LDPC code coding method of low complex degree, carries out decoding initialization first, and then iteration carries out as follows
Step：Hard decision, side information are calculated, check node calculation and variable node are calculated, until successfully decoded or failure；Its feature
It is that described interpretation method, code-word symbol are represented using binary form, and including following aspect：
1）During decoding initialization, weighted factor is set, codeword information is initialized using bit confidence coefficient；
2）The confidence level of the outside verification sum on check-node and variable node connection side is converted into bit confidence coefficient vector, participates in becoming
Amount node is calculated；
3）The codeword information and the external information of check-node that iteration updates every time is all bit confidence coefficient vector；
Described interpretation method, when on side, information is calculated, side information includes the multi-system hard decision symbol of code word external information and is somebody's turn to do
The confidence level of symbol；Wherein, the confidence level of symbol is all minimizations of the sum of absolute value in the binary digit external information of code word；
Described interpretation method, when variable node is calculated, the information of check-node input variable node, using based on Hamming distance
From confidence level weighting scheme obtaining, specifically：The two of sum is verified according to check-node and the outside of variable node connection side
System represent and Hamming distance between the binary representation of code-word symbol hard decision size setting weighted factor, using weighting
The confidence level of the outside verification sum on factor pair connection side is weighted.
2. m-ary LDPC code coding method according to claim 1, it is characterised in that in described interpretation method, institute
There is the information that codeword information, code word external information, the confidence level of outside verification sum and check-node input to variable node to be
Integer.
3. m-ary LDPC code coding method according to claim 1, it is characterised in that described use bit confidence coefficient
Codeword information is initialized, specifically：Binary message y of the code word that system is received is with quantized interval and quantization
Bit numberωUniform quantization is assigned to the codeword information of the 1st iteration for integer.
4. m-ary LDPC code coding method according to claim 1, it is characterised in that the outer letter of described check-node
Breath, specifically：During the 1st iteration, the of check-nodejThe binary digit external information of individual code-word symbol is equal to first time iteration
ThejThe binary piece of information of individual code-word symbol；ThekDuring secondary iteration,k>=2, the of check-nodejThe binary system of individual code-word symbol
Position external information is by thekThe codeword information of secondary iteration deductskCheck-node input the during -1 iterationjThe information of individual variable node
Obtain.
5. m-ary LDPC code coding method according to claim 1, it is characterised in that described check node calculation
When, the side for connecting check-node and variable node includes two parts information：Part I is that the outside of the side verifies and second
It is divided into outside the side and verifies the confidence level of sum；Wherein, outside the side, the determination method of the confidence level of verification sum is：First, obtain
The minimum value MIN of confidence level in all sides being connected with check-node1With sub-minimum MIN2, the confidence level being connected with check-node
The confidence level of the outside verification sum on minimum side is MIN2, the side that residue is connected with check-node it is outside verify and confidence level
It is MIN1。
6. m-ary LDPC code coding method according to claim 4, it is characterised in that described codeword information, updates
Method is：ThekDuring+1 iterationjThe binary piece of information of individual code-word symbol, is obtained by two parts summation, and Part I is
During first time iterationjThe binary piece of information of individual code-word symbol, Part II are tokDuring secondary iteration, each check-node is defeated
Enter tojThe binary piece of information summation of individual variable node is obtained.
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| CN106301388B (en) * | 2015-05-14 | 2020-10-23 | 北京航空航天大学 | Decoding method of multi-system LDPC code |
| CN105763203B (en) * | 2016-02-14 | 2020-04-24 | 广西大学 | Multi-element LDPC code decoding method based on hard reliability information |
| CN105846833B (en) * | 2016-04-13 | 2019-06-25 | 国家电网公司 | A kind of weighted messages transmitting interpretation method based on becate distribution |
| CN106856406B (en) * | 2016-11-18 | 2020-05-15 | 北京航空航天大学 | Method for updating check node in decoding method and decoder |
| CN106936446A (en) * | 2017-03-10 | 2017-07-07 | 南京大学 | A kind of high speed decoder and its interpretation method based on Non-Binary LDPC Coded |
| CN106936445B (en) * | 2017-03-14 | 2019-06-21 | 西安电子科技大学 | A kind of multielement LDPC code coding method of low complex degree near-maximum-likelihood |
| CN107124186B (en) * | 2017-03-17 | 2020-06-19 | 上海交通大学 | Two-stage decoding method of LDPC code based on grid complexity |
| CN108768410A (en) * | 2018-06-08 | 2018-11-06 | 中国电子科技集团公司第五十八研究所 | A kind of check-node update method suitable for Non-Binary LDPC Coded |
| CN109714060A (en) * | 2018-12-26 | 2019-05-03 | 西安烽火电子科技有限责任公司 | A kind of adaptive decoding method that LDPC code can be translated suitable for majority logic |
| CN111384975B (en) * | 2018-12-29 | 2023-05-26 | 泰斗微电子科技有限公司 | Optimization method, device and decoder of multi-system LDPC decoding algorithm |
| CN114421972B (en) * | 2022-01-27 | 2022-11-22 | 石家庄市经纬度科技有限公司 | Decoding method of multi-system LDPC code |
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