CN107241104A - One local contrary sign dynamic BP interpretation method for LDPC code - Google Patents

One local contrary sign dynamic BP interpretation method for LDPC code Download PDF

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CN107241104A
CN107241104A CN201710270488.3A CN201710270488A CN107241104A CN 107241104 A CN107241104 A CN 107241104A CN 201710270488 A CN201710270488 A CN 201710270488A CN 107241104 A CN107241104 A CN 107241104A
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variable node
message
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CN107241104B (en
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龚怡
江颖
凌捷
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Guangdong University of Technology
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1105—Decoding
    • H03M13/1111—Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms
    • H03M13/1125—Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms using different domains for check node and bit node processing, wherein the different domains include probabilities, likelihood ratios, likelihood differences, log-likelihood ratios or log-likelihood difference pairs

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  • Probability & Statistics with Applications (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
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Abstract

The present invention is directed to the dynamic BP decoding algorithm of LDPC code, propose a kind of local dynamic station based on LDPC code and update interpretation method (LILRBP), this method uses the information updating based on local residual error, effectively improve including the BP decoding performances in a small amount of iterations and under high s/n ratio, surmounted other dynamic BP decoding algorithms.From unlike conventional dynamic BP interpretation method, it is ageing that LILRBP methods think that residual error has, therefore time upper this nearest part residual error is only focused on, and set iterations threshold value, under threshold value, local residual error is screened again according to correlated variables node likelihood ratio sign change situation, next message to be updated then is determined by the residual error filtered out；Next message to be updated directly then is determined by local residual error on threshold value.Advantage of this is that total energy uses newest message to carry out information updating, play a part of accelerating algorithm convergence rate, and local residual error is screened again under threshold value, even more further speed up algorithmic statement, both combine joint effect convergence, the convergence rate of BP decoding algorithms is effectively improved, the purpose of lifting decoding performance is reached.

Description

One local contrary sign dynamic BP interpretation method for LDPC code
Technical field
The present invention relates to a kind of LDPC code decoding technique field, more particularly to a kind of local contrary sign dynamic based on LDPC code Interpretation method.
Background technology
Since LDPC code was found again from 1996, its decoding algorithm (flooding BP algorithms) is simple with its realization, The features such as decoding complexity is linearly increasing, becomes coding and decoding field focus.And SVNF-RBP algorithms are translated for the dynamic BP of representative Although code algorithm adds residual computations and search complexity, while also greatly improving the decoding performance of BP algorithm.
SVNF-RBP decoding algorithms are an asynchronous dynamical message iterative algorithms, each time according to a maximum verification section Point arrives variable node message residual error, positions next check-node to be updated to variable node message.Information updating is exactly root It is sequence according to the maximum residul difference found every time, is transmitted back and forth along the side in the Tanner figures corresponding with LDPC code, its message is passed Main two steps of lateral calculations and longitudinal direction calculating included for each variable node are passed, wherein lateral calculations are exactly school Test node ciTo variable node vjMessage transmission：
It is exactly variable node v that longitudinal direction, which is calculated,iTo check-node cjMessage transmission：
It is finally that 0,1 judgement is done by the maximum likelihood ratio of each variable node in BP decoding algorithms.Each Variable node will all receive the prior probability for carrying out self-channel(pv(0), pv(1) represent to pass respectively The bit passed is 0 and 1 probability), also to receive the message from each check-node transmission being attached thereto.Therefore variable Node viLikelihood ratio be exactly all message summations received：
Likelihood ratio message residual computations formula：r(mk)=| | fk(m)-mk||∞, mk∈m；Wherein m represents to calculate fk(m) institute The related news needed, mkAnd fk(m) likelihood ratio before check-node updates to variable node and after renewal is represented respectively.
SVNF-RBP algorithm iterations process stops in a period of time for meeting following condition：
(1) all check equations are all met.
(2) iterations reaches the maximum of setting.
The detailed process of SVNF-RBP algorithms is：
1) all m are initializedc,v=0；
2) initialize all
3) all r (m are calculatedc,v)；
4) to each vj, find out
5) calculateWithca∈N(vmax)\cmax
6) calculateca∈N(vmax)\cmax,vb∈N(ca)\vmax
If 7) all check equations meet or reached the maximum iteration of setting, terminate decoding, otherwise return Step 4)
For BP iterative algorithms, asynchronous strategy is typically all by accelerating decoding convergence to lift decoding performance.SVNF- BP decoding performances can be substantially improved in RBP algorithms, but are the increase in substantial amounts of calculating, search complexity.Therefore, in lifting decoding property Reduction complexity is particularly important while energy.
The content of the invention
It is an object of the invention to overcome at least one shortcoming and deficiency of above-mentioned prior art there is provided one kind to be based on LDPC The local dynamic station interpretation method of code, the local contrary sign dynamic decoding method effectively improves the decoding under especially high s/n ratio Can, while reducing residual error search and storage complexity.
The purpose of the present invention is achieved through the following technical solutions：
A kind of dynamic BP interpretation method based on LDPC code, proposes that residual error has ageing, and sets iterations threshold value, In the range of the local residual error of newest generation, when iterations is less than threshold value, with reference to the likelihood ratio symbol of correlated variables node Change is screened to local residual error again, and the update sequence that maximum residul difference determines message is found out in the residual error filtered out；When repeatedly When generation number is higher than threshold value, the update sequence that the maximum determines message is found out in local residual error.
The check-node to be updated is selected to variable node messageNew information firstTo all verification sections Point ca∈N(vj)\ciProduce and transmit messageTo all variable node vb∈N(ca)\vjCalculate message residual error When iterations is less than iterations threshold value IthrWhen, allIn find out variable node vbLikelihood ratio symbol will The residual error changed, and find out the maximum wherein and determine next check-node to be updated to variable node message；When Iterations is more than iterations threshold value IthrWhen, allIn find out the maximum and determine next verification to be updated Node is to variable node message.
Local contrary sign dynamic decoding algorithm (LILRBP)：
1) all m are initializedc,v=0
2) initialize all
3) all r (m are calculatedc,v)
4) in all r (mc,v) in find out the related residual for the v that likelihood ratio symbol can change, and find out wherein
5) calculateWithca∈N(vmax)\cmax
6) calculateca∈N(vmax)\cmax,vb∈N(ca)\vmax
7) I ＜ IthrWhen, allIn find out the v that likelihood ratio symbol can changebRelated residual, and Find out whereinI ＞ IthrWhen, allIn find out
If 8) all check equations meet or reached the maximum iteration of setting, terminate decoding, otherwise return Step 5)
Wherein：mc,vRefer to all check-nodes to the message of variable node；Refer to variable node vnIt is connected to all Check-node message；Represent variable node viChannel prior probability；r(mc,v) refer to all check-nodes to variable Residual error before the information updating of node and after renewal；Represent check-node ciTo variable node vjLikelihood ratio update Residual error after preceding and renewal；N(vi) represent and variable node viConnected all check-node set, check-node ca∈N(vi) Represent check-node caTo take all over variable node viBe connected all check-nodes；Represent from check-node caTo variable section Point viMessage,Represent from variable node viTo check-node cjMessage；N(cj) represent and check-node cjConnected institute There are variable node, N (cj)\viRepresent and check-node cjConnected is all not including variable node viOther variable nodes, vb ∈N(cj)\viRepresent variable node vbTo take all over check-node cjConnected is all not including variable node viIts dependent variable Node；I represents iterations, and IthrIt is iterations threshold value.
Likelihood ratio message residual computations formula：r(mk)=| | fk(m)-mk||∞, mk∈m；Wherein m represents to calculate fk(m) institute The related news needed, mkAnd fk(m) likelihood ratio before check-node updates to variable node and after renewal is represented respectively.
It is ageing that this method proposes that the generation of residual error has, and sets iterations threshold value, using the threshold value as boundary, iteration time When number is less than threshold value, screened in local residual error scope in conjunction with the likelihood ratio sign change situation of correlated variables node, And find out maximum residul difference to set up a check-node to the renewal sequence of variable node message in these residual errors selected；Repeatedly When generation number is higher than threshold value, maximum residul difference is found out in local residual error to set up a check-node to variable node message more New sequence,
Therefore, the present invention has the following advantages and effect relative to prior art：
The residual error of maximum is only found out from the residual error of newest generation, can be scanned for while calculating, therefore residual error is not Storage is needed, storage complexity is reduced；The namely local residual error of the residual error of newest generation, reduces answering for search maximum residul difference Miscellaneous degree；Less than iterations threshold value, local residual error always can ensure that the information updating that next step is carried out using latest news, and office The residual error that portion's residual error combination variable node likelihood ratio sign change situation is filtered out again, can further accelerate variable node and turn over Turn, reach the convergence rate for accelerating decoding process.
Relative to SVNF-RBP algorithms, the present invention can not only improve the decoding performance of less iterations, more greatly Improve the decoding performance of high s/n ratio.
Brief description of the drawings
Fig. 1 is algorithm LILRBP dynamic strategy schematic diagram.
Fig. 2 is algorithm flooding, LBP, and NW RBP, SVNF-RBP and LILRBP are in code length 1944, code checkGiven letter The FER performance maps made an uproar during than for 1.75dB.
Fig. 3 is algorithm SVNF-RBP and LILRBP in code length 1944, code check5th, FER performance maps during 50 iteration.
Embodiment
With reference to embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited In this.
The present invention is a kind of local dynamic station interpretation method based on LDPC code, is the local contrary sign dynamic BP for LDPC code Interpretation method (LILRBP), it is ageing that this method proposes that the generation of residual error has, and only focuses on the local residual error of nearest time generation, And iterations threshold value is set, when iterations is less than threshold value, the change of correlated variables node likelihood ratio is combined in local residual error Situation screening residual error is changed, and finds out maximum residul difference to set up a check-node to variable node message in the residual error filtered out Renewal sequence；When iterations is higher than threshold value, directly find out maximum residul difference in local residual error to set up a check-node To the renewal sequence of variable node message.
If I represents iterations, and IthrIt is iterations threshold value；N(vi) represent and variable node viConnected all schools Test node, N (vi)\cjThen represent and variable node viConnected does not include check-node cjEvery other check-node；N(ci) Represent and check-node (check equations) ciConnected all variable nodes, N (ci)\vjThen represent and check-node ciConnected Do not include variable node vjEvery other variable node.The variable node and check-node Message function definable of interconnection ForWherein m represents to calculateOrRequired related news. The prior probability of channel(pv(0), pv(1) bit information for representing transmission respectively is 0 and 1 Probability).Check-node is to variable node likelihood ratio message residual computations formula r (mk)=| | fk(m)-mk||∞, wherein m represents Calculate fk(m) related news needed for, mkAnd fk(m) represent respectively before check-node updates to variable node message and after renewal Likelihood ratio.
Assuming that check-node is to variable node messageWith local maxima residual error, the dynamic strategy bag of the decoding algorithm Include following three step：
First, new informationAnd transmit.
Secondly, new informationca∈N(vj)\ciAnd transmit.
Finally, residual error is calculatedvb∈N(ca)\vj,ca∈N(vj)\ci, as I ＜ IthrWhen, all In find out the v that likelihood ratio symbol can changebRelated residual, and find out maximum residul difference wherein；I ＞ IthrWhen, institute HaveIn find out maximum residul difference.
Specifically, algorithm iteration process of the invention is as follows：
1) all m are initializedc,v=0
2) initialize all
3) all r (m are calculatedc,v)
4) in all r (mc,v) in find out the related residual for the v that likelihood ratio symbol can change, and find out wherein
5) calculateWithca∈N(vmax)\cmax
6) calculateca∈N(vmax)\cmax,vb∈N(ca)\vmax
7) I ＜ IthrWhen, allIn find out the v that likelihood ratio symbol can changebRelated residual, and Find out whereinI ＞ IthrWhen, allIn find out
If 8) all check equations meet or reached the maximum iteration of setting, terminate decoding, otherwise return Step 5)
During an iteration of dynamic BP decoding algorithm, otherwise check-node to variable node message amount of calculation with BP algorithm is identical, or the message amount of calculation of variable node to check-node is identical with BP algorithm, all emulation all will be strict In accordance with this rule.Following table provides the message amount of calculation to this algorithm an iteration process, wherein,WithRepresent to become respectively The average degree of node and check-node is measured, e represents the quantity on side in Tanner figures, had simultaneouslyInto Vertical, wherein N and M represent the number of variable node and check-node in Tanner figures respectively.
Check-node in an iteration of table 1 is to variable node message amount of calculation
Variable node in an iteration of table 2 is to check-node message amount of calculation
In table 1,2, Flooding BP algorithms are used as asynchronous non-dynamic message as synchronization message more new algorithm, LBP algorithms More new algorithm, is only referred to.
Dynamic algorithm NW RBP algorithms and SVNF-RBP algorithms are all residual to variable node message maximum using check-node Difference, maximum residul difference calculation formula：r(mk)=| | fk(m)-mk||∞, wherein r (mk) maximum message residual error is represented, m represents to calculate fk (m) related news needed for, mkAnd fk(m) likelihood ratio before check-node updates to variable node and after renewal is represented respectively, is come Next check-node to be updated is found out to variable node message, then deploys the information updating process of an essence, two Algorithm is required for storing residual error, except that NW RBP algorithms are to disappear in whole non-zero check-nodes to variable node Next message preferentially to update is chosen in breath residual error, and SVNF-RBP algorithms are in each variable node coverage Non-zero check-node next message preferentially to update is chosen into variable node message residual error.
Related algorithm principal character is given below：
NW RBP algorithms：
1) all m, are initializedc,v=0；
2), initialize all
3) all r (m, are calculatedE, v)；
4), maximum residul difference is selected in all non-zero residual errors
5), to each vk∈N(ci), calculateWhile handleIt is set to 0.
6), to each ca∈N(vk), calculate
7), to each vb∈N(ca)\vk, calculate
If 8), all check equations meet or reached the maximum iteration of setting, then terminate decoding, otherwise return Return step 4.
SVNF-RBP algorithms：
1) all m, are initializedc,v=0；
2), initialize all
3) all r (m, are calculatedE, v)；
4), to each vi, to all vb∈N(ca)\vi(ca∈N(vi)), in all non-zero residual errorsIn select Maximum residul difference
5), calculateAnd set
6), to each ca∈N(vmax)\cmax, calculate
7), to each vb∈N(ca)\vmax, calculate
If 8), all check equations meet or reached the maximum iteration of setting, then terminate decoding, otherwise return Return step 4.
It can be seen that from above-mentioned arthmetic statement, the LILRBP algorithms and NW RBP and SVNF-RBP algorithm all use check-node To variable node likelihood ratio absolute residuals localization method, the difference is that the time that LILRBP algorithms difference residual error is produced, only makes With the residual error of newest generation；And it is indifference pair that the residual error that NW RBP and SVNF-RBP algorithm are produced to different time, which is given, Treat, all residual errors are made no exception.In view of SVNF-RBP be in current dynamic algorithm it is most representational, therefore LILRBP calculates Method will be contrasted mainly with SVNF-RBP algorithms.
As shown in figure 1, black circles represent the variable node being updated, black box represents the school being updated Test node.Dynamic asynchronous information updating strategy step is as follows, first as shown in Fig. 1 (a), selects check-node and disappears to variable node BreathIt is preferential to update, wherein variable node vjLikelihood ratio symbol will change, then as shown in Fig. 1 (b), to all schools Test node ca∈N(vj)\ciProduce messageAnd transmitted, finally, Fig. 1 (c), to all check-node ca∈N(vj)\ ci, vb∈N(ci)\vjCalculate residual errorWhich variable node v determined simultaneouslybLikelihood ratio symbol will change.
Fig. 2 lists NW RBP, SVNF-RBP and LILRBP including Flooding BP, LBP in code length 1944, Code checkThe iterations threshold value I of FER performance maps, wherein LILRBP algorithms when given signal to noise ratio is 1.75dBthrIt is set as 10.It can be seen that LILRBP performance curves in 5 iteration are obvious under SVNF-RBP algorithm curves, and SVNF-RBP is most representative dynamic decoding algorithm, therefore the main and SVNF-RBP algorithms in analogous diagram below at present Contrasted.All emulation are carried out under awgn channel.
Fig. 3 gives code length 1944, code checkWhen, respectively 5, under 50 iterationses, SVNF-RBP and LILRBP algorithms FER performance maps, wherein LILRBP algorithms iterations threshold value IthrIt is set as 10.It can be seen that LILRBP algorithms In less 5 iteration of iterations, decoding performance has been slightly better than SVNF-RBP algorithms, and performance is substantially better than during high s/n ratio SVNF-RBP algorithms, in 50 iteration in the case of low signal-to-noise ratio, performance and SVNF-RBP algorithms are basically identical, middle and high SVNF-RBP algorithms are surmounted during signal to noise ratio, especially in high s/n ratio, performance far wins SVNF-RBP algorithms.
The present invention discloses a kind of local contrary sign dynamic decoding method --- LILRBP (Local based on LDPC code Inverse and Local Residual BP), this method can not only reduce search and the storage complexity of residual error, also simultaneously The decoding performance (SVNF-RBP algorithms are in smaller iterations almost without performance boost) in smaller iterations can be lifted, Decoding performance is also significantly better than SVNF-RBP algorithms during high s/n ratio.
It is ageing that LILRBP algorithms think that residual error has, that is, the residual error that different time is produced, and it acts on also phase not to the utmost Together.LILRBP algorithms only focus on the residual error of newest generation, and set iterations threshold value, when iterations is less than threshold value, then In the residual error of newest generation, residual error is screened according to correlated variables node likelihood ratio sign change situation, found out most Big residual error sets up check-node to the renewal sequence of variable node message；When iterations is higher than threshold value, directly newest Maximum residul difference is found out in the residual error of generation to set up check-node to the renewal sequence of variable node message.Due to newest generation Residual error is, by newest information updating generation, therefore always to can ensure that and gone to update next message with newest message, play plus The convergent effect of speed, and screened again with reference to variable node likelihood ratio sign change situation, further reinforcing accelerates convergence Effect, improve decoding performance.Meanwhile, maximum residul difference is searched in newest residual error, can be carried out while calculating, therefore be not required to Residual error is stored, the scope of search reduces, and effectively reduces the storage search complexity of dynamic decoding algorithm.
Above-described embodiment is preferably embodiment, but embodiments of the present invention are not by above-described embodiment of the invention Limitation, other any Spirit Essences without departing from the present invention and the change made under principle, modification, replacement, combine, simplification, Equivalent substitute mode is should be, is included within protection scope of the present invention.

Claims (4)

1. a kind of local contrary sign dynamic BP interpretation method based on LDPC code, it is characterised in that iterations threshold value is set, most In the range of the local residual error newly produced, when iterations is less than threshold value, with reference to the likelihood ratio sign change of correlated variables node Local residual error is screened again, the update sequence that maximum residul difference determines message is found out in the residual error filtered out；When iteration time When number is higher than threshold value, the update sequence that the maximum determines message is found out in local residual error.
2. the local contrary sign dynamic BP interpretation method according to claim 1 based on LDPC code, it is characterised in that selected to want The check-node of renewal is to variable node message(wherein variable node vjLikelihood ratio symbol update after will become Change), new information firstTo all check-node ca∈N(vj)\ciProduce and transmit messageTo all variable sections Point vb∈N(ca)\vjCalculate messageLocal residual error, iterations be less than iteration threshold when combine correlated variables node seemingly Right ratio sign change is screened again to local residual error, is then found out maximum residul difference and is determined next check-node to be updated to change Measure node messages；When iterations is more than iteration threshold, the maximum is directly found out in local residual error and determines next to update Check-node to variable node message；Wherein, N (vj) represent and variable node vjConnected all check-node set, N (vj)\ciRepresent and variable node vjConnected is all except check-node ciOuter check-node, check-node ca∈N(vj)\ci Represent check-node caTo take all over variable node vjConnected is all except check-node ciOuter check-node；N(ca) represent with Check-node caConnected all variable nodes, N (ca)\vjRepresent and check-node caConnected is all except variable node vjOuter Variable node, vb∈N(ca)\vjRepresent variable node vbTo take all over check-node caConnected is all except variable node vjOuter Variable node.
3. the local contrary sign dynamic BP interpretation method according to claim 2 based on LDPC code, it is characterised in that
Local contrary sign dynamic decoding algorithm (LILRBP)：
1) all m are initializedc,v=0；
2) initialize all
3) all r (m are calculatedc,v)；
4) in all r (mc,v) in find out the related residual for the v that likelihood ratio symbol can change, and find out wherein5) calculateWithca∈N(vmax)\cmax；
6) calculateca∈N(vmax)\cmax,vb∈N(ca)\vmax；
7) I ＜ IthrWhen, allIn find out the v that likelihood ratio symbol can changebRelated residual, and at it In find outI ＞ IthrWhen, allIn find out
If 8) all check equations meet or reached the maximum iteration of setting, terminate decoding, otherwise return to step 5)；Wherein：mc,vRefer to all check-nodes to the message of variable node；Refer to variable node vnTo all connected verifications The message of node；Represent variable node viChannel prior probability；r(mc,v) refer to all check-nodes to variable node Residual error before information updating and after renewal；Represent check-node cjTo variable node viLikelihood ratio update before and more Residual error after new；N(vi) represent and variable node viConnected all check-node set, N (vi)\cjRepresent and variable node vi Connected is all except check-node cjOuter check-node, check-node ca∈N(vi)\cjRepresent check-node caTo take all over change Measure node viConnected is all except check-node cjOuter check-node；Represent from check-node caTo variable node vi's Message,Represent from variable node viTo check-node cjMessage；N(cj) represent and check-node cjConnected all changes Measure node, N (cj)\viRepresent and check-node cjConnected is all except variable node viOuter variable node, vb∈N(cj)\vi Represent variable node vbTo take all over check-node cjConnected is all except variable node viOuter variable node；I represents iteration time Number, and IthrIt is iterations threshold value.
4. the local contrary sign dynamic BP interpretation method according to claim 3 based on LDPC code, it is characterised in that by seeking Local maxima residual error is looked for set up a check-node to the renewal sequence of variable node message, likelihood ratio message residual computations public affairs Formula：r(mk)=| | fk(m)-mk||∞, mk∈m；Wherein m represents to calculate fk(m) related news needed for, mkAnd fk(m) generation respectively Likelihood ratio before table check-node updates to variable node and after renewal.
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