CN107241104B - Local different-sign dynamic BP decoding method for LDPC code - Google Patents

Local different-sign dynamic BP decoding method for LDPC code Download PDF

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CN107241104B
CN107241104B CN201710270488.3A CN201710270488A CN107241104B CN 107241104 B CN107241104 B CN 107241104B CN 201710270488 A CN201710270488 A CN 201710270488A CN 107241104 B CN107241104 B CN 107241104B
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龚怡
江颖
凌捷
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Guangdong University of Technology
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    • 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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Abstract

The invention provides a local dynamic update decoding method (LILRBP) based on LDPC codes aiming at the dynamic BP decoding algorithm of the LDPC codes, and the method adopts message update based on local residual errors, thereby effectively improving the BP decoding performance in a small number of iteration times and under a high signal-to-noise ratio and surpassing other dynamic BP decoding algorithms. Different from the traditional dynamic BP decoding method, the LILRBP method considers that the residual error has timeliness, so that only the part of the residual error which is nearest in time is concerned, an iteration time threshold value is set, the local residual error is screened according to the sign change condition of the likelihood ratio of the related variable nodes under the threshold value, and then the next message to be updated is determined according to the screened residual error; above the threshold the next message to be updated is determined directly from the local residual. The advantage of doing so is that can always use the newest message to carry on the message renewal, play the role of accelerating the convergence rate of the algorithm, and screen the local residual error again under the threshold value, it is the convergence of further acceleration algorithm, both combine the convergence nature that influences the algorithm together, have improved the convergence rate of BP decoding algorithm effectively, achieve the goal of promoting the decoding performance.

Description

Local different-sign dynamic BP decoding method for LDPC code
Technical Field
The invention relates to the technical field of LDPC code decoding, in particular to a local different-sign dynamic decoding method based on an LDPC code.
Background
Since the LDPC code was discovered again in 1996, the decoding algorithm (flooding BP algorithm) becomes a focus in the field of encoding and decoding due to its simple implementation and linear increase of decoding complexity. Although the dynamic BP decoding algorithm represented by the SVNF-RBP algorithm increases the complexity of residual calculation and search, the decoding performance of the BP algorithm is greatly improved.
The SVNF-RBP decoding algorithm is an asynchronous dynamic message iteration algorithm, and the next check node to variable node message to be updated is positioned according to a maximum check node to variable node message residual error each time. The message updating is to pass back and forth along the edge in the Tanner graph corresponding to the LDPC code according to the sequence of the maximum residual error found each time, and the message passing mainly comprises two steps of horizontal calculation and vertical calculation for each variable node, wherein the horizontal calculation is the check node ciTo variable node vjThe message passing of (2):
Figure BDA0001277230670000011
the longitudinal calculation is a variable node viTo check node cjThe message passing of (2):
Figure BDA0001277230670000012
in the BP decoding algorithm, the maximum likelihood ratio of each variable node is finally relied on to make 0 and 1 judgments. Each variable node will receive a prior probability from the channel
Figure BDA0001277230670000013
(pv(0)，pv(1) Representing the probability of 0 and 1, respectively, of the transmitted bit) and also receives the transmitted message from each check node connected thereto. Node v of the variableiThe likelihood ratio of (a) is the sum of all received messages:
Figure BDA0001277230670000014
likelihood ratio message residual calculation formula: r (m)k)＝||fk(m)-mk||∞，mkE is m; wherein m represents the calculation fk(m) required correlation messages, mkAnd fk(m) represent likelihood ratios before and after the check node to variable node update, respectively.
The SVNF-RBP algorithm iteration process stops when one of the following conditions is met:
(1) all the check equations are satisfied.
(2) The iteration number reaches the set maximum value.
The specific process of the SVNF-RBP algorithm is as follows:
1) initialize all mc,v＝0；
2) Initialize all
Figure BDA00012772306700000211
3) Calculate all r (m)c,v)；
4) For each vjFind out
Figure BDA0001277230670000021
5) Computing
Figure BDA0001277230670000022
And
Figure BDA0001277230670000023
ca∈N(vmax)\cmax
6) computing
Figure BDA0001277230670000024
ca∈N(vmax)\cmax,vb∈N(ca)\vmax
7) If all the check equations meet or reach the set maximum iteration number, ending the decoding, otherwise, returning to the step 4)
For BP iterative algorithm, the asynchronous strategy generally promotes decoding performance by accelerating decoding convergence. The SVNF-RBP algorithm can greatly improve BP decoding performance, but increases a large amount of calculation and search complexity. Therefore, it is important to reduce complexity while improving decoding performance.
Disclosure of Invention
The present invention is directed to overcome at least one of the disadvantages and shortcomings of the prior art, and to provide a local dynamic decoding method based on LDPC codes, which effectively improves decoding performance especially at high snr, and reduces complexity of residual search and storage.
The purpose of the invention is realized by the following technical scheme:
a dynamic BP decoding method based on LDPC code, propose the residual error has timeliness, and set up the threshold value of iteration number, in the local residual error range produced recently, when the iteration number is lower than the threshold value, combine the likelihood ratio sign change of the relevant variable node and carry on the screening to the local residual error again, find out the maximum residual error in the residual error screened and confirm the renewal order of the message; when the iteration number is higher than a threshold value, finding the largest one in the local residuals to determine the updating sequence of the messages.
Selecting check node to variable node messages to update
Figure BDA0001277230670000025
First updating the message
Figure BDA0001277230670000026
For all check nodes ca∈N(vj)\ciGenerating and delivering messages
Figure BDA0001277230670000027
For all variable nodes vb∈N(ca)\vjComputing message residuals
Figure BDA0001277230670000028
When the iteration number is less than the iteration number threshold IthrAt all time, in
Figure BDA0001277230670000029
Find variable node v inbResidual errors of which the likelihood ratio signs are changed are found out, and the maximum residual error is found out to determine the message from the next check node to the variable node to be updated; when the iteration number is larger than the iteration number threshold value IthrAt all time, in
Figure BDA00012772306700000210
The largest one is found in the check nodes to determine the next check node to variable node message to be updated.
Local alien dynamic decoding algorithm (LILRBP):
1) initialize all mc,v＝0
2) Initialize all
Figure BDA0001277230670000031
3) Calculate all r (m)c,v)
4) At all r (m)c,v) Finding out the residual error of v whose likelihood ratio sign can be changed and finding out the residual error
Figure BDA0001277230670000032
5) Computing
Figure BDA0001277230670000033
And
Figure BDA0001277230670000034
ca∈N(vmax)\cmax
6) computing
Figure BDA0001277230670000035
ca∈N(vmax)\cmax,vb∈N(ca)\vmax
7)I＜IthrAt all time, in
Figure BDA0001277230670000036
Finding v with changed likelihood ratio signbAnd finding out the related residual error therein
Figure BDA0001277230670000037
I＞IthrAt all time, in
Figure BDA0001277230670000038
In the process of finding
Figure BDA0001277230670000039
8) If all the check equations meet or reach the set maximum iteration number, ending the decoding, otherwise, returning to the step 5)
Wherein: m isc,vThe messages from all check nodes to variable nodes are generally referred to;
Figure BDA00012772306700000310
generalized variable node vnTo all connected check nodesA message;
Figure BDA00012772306700000311
representing variable node viA channel prior probability of (d); r (m)c,v) The residual errors before and after the update of the messages from all the check nodes to the variable nodes are generally referred to;
Figure BDA00012772306700000312
represents check node ciTo variable node vjBefore and after updating the likelihood ratio value of (a); n (v)i) Representation and variable node viAll connected check node sets, check node ca∈N(vi) Represents check node caWill take the sum of the variable node viConnecting all check nodes;
Figure BDA00012772306700000313
representing slave check node caTo variable node viThe message of (a) is received,
Figure BDA00012772306700000314
representing a slave variable node viTo check node cjThe message of (2); n (c)j) Representing and checking node cjAll variable nodes connected, N (c)j)\viRepresenting and checking node cjAll non-variable-included nodes v connectediOther variable node of vb∈N(cj)\viRepresenting variable node vbWill take and check node cjAll non-variable-included nodes v connectediOther variable nodes of (2); i denotes the number of iterations, and IthrIs the iteration number threshold.
Likelihood ratio message residual calculation formula: r (m)k)＝||fk(m)-mk||∞，mkE is m; wherein m represents the calculation fk(m) required correlation messages, mkAnd fk(m) represent likelihood ratios before and after the check node to variable node update, respectively.
The method provides that the generation of residual errors has timeliness, sets an iteration number threshold, screens the local residual error range in combination with the likelihood ratio sign change condition of relevant variable nodes when the iteration number is lower than the threshold by taking the threshold as a boundary, and finds out the maximum residual error in the selected residual errors to establish an updating sequence of messages from check nodes to variable nodes; when the iteration number is higher than the threshold value, finding out the maximum residual error in the local residual errors to establish an updating sequence of the messages from the check node to the variable node,
therefore, compared with the prior art, the invention has the following advantages and effects:
the maximum residual error is found out from the newly generated residual errors, and the search can be carried out while calculation is carried out, so that the residual errors do not need to be stored, and the storage complexity is reduced; the newly generated residual error is also the local residual error, so that the complexity of searching the maximum residual error is reduced; when the local residual error is lower than the threshold value of the iteration times, the next message updating can be carried out by using the latest message, and the residual error is screened out by combining the local residual error with the variable node likelihood ratio sign change condition, so that the variable node turnover can be further accelerated, and the convergence speed in the decoding process can be accelerated.
Compared with the SVNF-RBP algorithm, the invention can not only improve the decoding performance with less iteration times, but also greatly improve the decoding performance with high signal-to-noise ratio.
Drawings
Fig. 1 is a schematic diagram of the dynamic strategy of the algorithm LILRBP.
FIG. 2 shows the algorithm flooding, LBP, NW RBP, SVNF-RBP and LILRBP at code length 1944, code rate
Figure BDA0001277230670000041
FER performance plot given signal-to-noise ratio of 1.75 dB.
FIG. 3 shows the algorithm SVNF-RBP and LILRBP at code length 1944, code rate
Figure BDA0001277230670000042
Figure BDA0001277230670000042
5. FER performance map at 50 iterations.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
The invention relates to a local dynamic decoding method based on LDPC codes, which is a local different sign dynamic BP decoding method (LILRBP) aiming at the LDPC codes, and the method provides that the generation of residual errors has timeliness, only pays attention to local residual errors generated in the latest time, sets an iteration time threshold, screens the residual errors in the local residual errors in combination with the likelihood ratio transformation condition of relevant variable nodes when the iteration time is lower than the threshold, and finds out the maximum residual error in the screened residual errors to establish an updating sequence of messages from check nodes to variable nodes; when the iteration times are higher than the threshold value, the maximum residual error is directly found out from the local residual errors to establish an updating sequence of the messages from the check nodes to the variable nodes.
Let I denote the number of iterations, and IthrIs an iteration number threshold; n (v)i) Representative and variable node viAll check nodes connected, N (v)i)\cjThen the representation and variable node viConnected nodes c not including check nodesjAll other check nodes of (1); n (c)i) Representation and check node (check equation) ciAll variable nodes connected, N (c)i)\vjThen the representing and checking node ciConnected nodes v not including variablesjAll other variable nodes. The interconnected variable node and check node message functions may be defined as
Figure BDA0001277230670000043
Wherein m represents the calculation
Figure BDA0001277230670000044
Or
Figure BDA0001277230670000045
The required related messages. Prior probability of channel
Figure BDA0001277230670000051
(pv(0)，pv(1) Representing the probability of 0 and 1, respectively, of the communicated bit information). Checking node to changeQuantity node likelihood ratio message residual error calculation formula r (m)k)＝||fk(m)-mk||∞Wherein m represents the calculation fk(m) required correlation messages, mkAnd fk(m) represent likelihood ratios before and after updating of check node to variable node messages, respectively.
Assume check node to variable node messages
Figure BDA0001277230670000052
With local maximum residual, the dynamic strategy of the decoding algorithm comprises the following three steps:
first, update the message
Figure BDA0001277230670000053
And transmitted.
Second, update messages
Figure BDA0001277230670000054
ca∈N(vj)\ciAnd transmitted.
Finally, the residual error is calculated
Figure BDA0001277230670000055
vb∈N(ca)\vj,ca∈N(vj)\ciWhen I < IthrAt all time, in
Figure BDA0001277230670000056
Finding v with changed likelihood ratio signbFinding the maximum residual error; i > IthrAt all time, in
Figure BDA0001277230670000057
Finding the largest residual error.
Specifically, the algorithm iteration process of the present invention is as follows:
1) initialize all mc,v＝0
2) Initialize all
Figure BDA00012772306700000516
3) Calculate all r (m)c,v)
4) At all r (m)c,v) Finding out the residual error of v whose likelihood ratio sign can be changed and finding out the residual error
Figure BDA0001277230670000058
5) Computing
Figure BDA0001277230670000059
And
Figure BDA00012772306700000510
ca∈N(vmax)\cmax
6) computing
Figure BDA00012772306700000511
ca∈N(vmax)\cmax,vb∈N(ca)\vmax
7)I＜IthrAt all time, in
Figure BDA00012772306700000512
Finding v with changed likelihood ratio signbAnd finding out the related residual error therein
Figure BDA00012772306700000513
I＞IthrAt all time, in
Figure BDA00012772306700000514
In the process of finding
Figure BDA00012772306700000515
8) If all the check equations meet or reach the set maximum iteration number, ending the decoding, otherwise, returning to the step 5)
Checking nodes to each other in one iteration process of dynamic BP decoding algorithmThe message computation amount of the variable nodes is the same as that of the BP algorithm, or the message computation amount of the variable nodes to the check nodes is the same as that of the BP algorithm, and all simulations strictly follow the rule. The following table gives the message computation for one iteration of this algorithm, where,
Figure BDA0001277230670000061
and
Figure BDA0001277230670000062
respectively representing the average degree of variable nodes and check nodes, and e represents the number of edges in the Tanner graph and has
Figure BDA0001277230670000063
And (4) establishing, wherein N and M respectively represent the number of variable nodes and check nodes in the Tanner graph.
TABLE 1 check node to variable node message computation in one iteration
Figure BDA0001277230670000064
TABLE 2 variable node to check node message computation in one iteration
Figure BDA0001277230670000065
In tables 1 and 2, the Flooding BP algorithm is used as the synchronous message update algorithm, and the LBP algorithm is used as the asynchronous non-dynamic message update algorithm, which is only referred to.
The dynamic algorithm NW RBP algorithm and the SVNF-RBP algorithm both adopt the maximum residual error of messages from check nodes to variable nodes, and the maximum residual error calculation formula is as follows: r (m)k)＝||fk(m)-mk||∞Wherein r (m)k) Denotes the maximum message residual, m denotes the calculation fk(m) required correlation messages, mkAnd fk(m) respectively representing likelihood ratios before and after updating of the check node to the variable node to find out the next check node to be updatedThe difference is that the NW RBP algorithm selects the next message to be preferentially updated from all non-zero check node to variable node message residuals, while the SVNF-RBP algorithm selects the next message to be preferentially updated from the non-zero check node to variable node message residuals in the coverage range of each variable node.
The main features of the correlation algorithm are given below:
NW RBP algorithm:
1) initializing all mc,v＝0；
2) Initializing all the devices
Figure BDA0001277230670000071
3) Calculating all r (m)e，v)；
4) Selecting the largest residual error from all non-zero residual errors
Figure BDA0001277230670000073
5) For each vk∈N(ci) Calculating
Figure BDA0001277230670000074
At the same time handle
Figure BDA0001277230670000075
Is set to 0.
6) For each one of ca∈N(vk) Calculating
Figure BDA0001277230670000076
7) For each vb∈N(ca)\vkCalculating
Figure BDA0001277230670000077
8) If all the check equations meet or reach the set maximum iteration number, ending the decoding, otherwise, returning to the step 4.
SVNF-RBP algorithm:
1) initializing all mc,v＝0；
2) Initializing all the devices
Figure BDA0001277230670000078
3) Calculating all r (m)e，v)；
4) For each viFor all vb∈N(ca)\vi(ca∈N(vi) At all non-zero residuals
Figure BDA00012772306700000710
To select the largest residual error
Figure BDA00012772306700000711
5) And calculating
Figure BDA00012772306700000712
And is provided with
Figure BDA00012772306700000713
6) For each one of ca∈N(vmax)\cmaxCalculating
Figure BDA00012772306700000714
7) For each vb∈N(ca)\vmaxCalculating
Figure BDA00012772306700000715
8) If all the check equations meet or reach the set maximum iteration number, ending the decoding, otherwise, returning to the step 4.
As can be seen from the above description of the algorithm, the LILRBP algorithm, the NW RBP algorithm, and the SVNF-RBP algorithm all use a check node to variable node likelihood ratio absolute residual error positioning method, except that the LILRBP algorithm distinguishes time of residual error generation and only uses the newly generated residual error; the NW RBP and SVNF-RBP algorithms give no difference to the residual errors generated at different times, and all the residual errors are treated identically. Considering that SVNF-RBP is the most representative of the current dynamic algorithms, the LILRBP algorithm will be compared with SVNF-RBP algorithm mainly.
As shown in fig. 1, the black circles represent variable nodes that have been updated, and the black boxes represent check nodes that have been updated. The dynamic asynchronous message updating strategy comprises the steps of firstly selecting a check node to variable node message as shown in figure 1(a)
Figure BDA0001277230670000081
Priority update in which variable node vjThe likelihood ratio sign will change and then, as shown in fig. 1(b), for all check nodes ca∈N(vj)\ciGenerating messages
Figure BDA0001277230670000082
And passed on, finally, FIG. 1(c), for all check nodes ca∈N(vj)\ci，vb∈N(ci)\vjCalculating residual error
Figure BDA0001277230670000083
Determining simultaneously which variable nodes vbThe likelihood ratio sign will change.
FIG. 2 lists the NW RBPs, SVNF-RBPs and LILRBP including the Flooding BP, LBP at code length 1944, code rate
Figure BDA0001277230670000084
FER performance map given 1.75dB signal-to-noise ratio, where the number of iterations of the LILRBP algorithm is threshold IthrSet to 10. As can be seen from the figure, the performance curve of LILRBP is obviously below the SVNF-RBP algorithm curve even in 5 iterations, and SVNF-RBP is the most representative dynamic decoding algorithm at present, so that the LILRBP is mainly compared with the SVNF-RBP algorithm in the later simulation graphs. All simulations were performed under AWGN channel.
FIG. 3 shows the code length 1944, code rate
Figure BDA0001277230670000085
Respectively under 5 and 50 times of iteration times, FER performance graphs of SVNF-RBP and LILRBP algorithms, wherein the iteration time threshold I of the LILRBP algorithmthrSet to 10. It can be seen from the figure that, in the LILRBP algorithm, when the number of iterations is less than 5, the decoding performance is slightly better than that of the SVNF-RBP algorithm, the performance is obviously better than that of the SVNF-RBP algorithm when the signal-to-noise ratio is high, and in the case of low signal-to-noise ratio in 50 iterations, the performance is basically consistent with that of the SVNF-RBP algorithm, and exceeds that of the SVNF-RBP algorithm when the signal-to-noise ratio is medium and high, especially when the signal-to-noise ratio is high, the performance is far better than that of the SVNF-.
The invention discloses a Local abnormal number dynamic decoding method based on LDPC codes, namely LILRBP (Local Inverse and Local Residual BP), which not only can reduce the complexity of searching and storing Residual errors, but also can improve the decoding performance within smaller iteration times (the SVNF-RBP algorithm has almost no performance improvement within the smaller iteration times), and the decoding performance is obviously superior to that of the SVNF-RBP algorithm at the time of high signal-to-noise ratio.
The LILRBP algorithm considers the residual to be time-efficient, that is, the residual generated at different times has different effects. The LILRBP algorithm only concerns the newly generated residual error, sets an iteration number threshold, and screens the residual error according to the sign change condition of the likelihood ratio of the related variable node in the newly generated residual error when the iteration number is lower than the threshold, and finds out the maximum residual error to establish an update sequence of the information from the check node to the variable node; when the iteration number is higher than the threshold value, the maximum residual error is directly found out from the newly generated residual errors to establish an updating sequence of the messages from the check nodes to the variable nodes. Because the newly generated residual error is generated by the updating of the latest message, the next message can be always updated by the latest message, the effect of accelerating convergence is achieved, and the re-screening is carried out by combining the symbol change condition of the likelihood ratio of the variable node, so that the effect of accelerating convergence is further strengthened, and the decoding performance is improved. Meanwhile, the maximum residual error in the latest residual errors can be searched while calculation is carried out, so that the residual errors do not need to be stored, the searching range is reduced, and the storage and searching complexity of the dynamic decoding algorithm is effectively reduced.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (1)

1. A local different-sign dynamic BP decoding method based on LDPC code is characterized in that an iteration number threshold is set, when the iteration number is lower than the threshold in a newly generated local residual error range, local residual errors are screened by combining likelihood ratio sign change of related variable nodes, and an updating sequence of a maximum residual error determination message is found out from the screened residual errors; when the iteration times are higher than a threshold value, finding out the largest one in the local residual errors to determine the updating sequence of the message;
selecting check node to variable node messages to update
Figure FDA0002601500210000011
First updating the message
Figure FDA0002601500210000012
For all check nodes ca∈N(vj)\ciGenerating and delivering messages
Figure FDA0002601500210000013
For all variable nodes vb∈N(ca)\vjComputing message residuals
Figure FDA0002601500210000014
When the iteration number is less than the iteration number threshold IthrAt all time, in
Figure FDA0002601500210000015
To find out the variableNode vbResidual errors of which the likelihood ratio signs are changed are found out, and the maximum residual error is found out to determine the message from the next check node to the variable node to be updated; when the iteration number is larger than the iteration number threshold value IthrAt all time, in
Figure FDA0002601500210000016
Finding out the largest one in the data to determine the message from the next check node to the variable node to be updated;
local alien dynamic decoding algorithm (LILRBP):
1) initialize all mc,v＝0
2) Initialize all
Figure FDA0002601500210000017
3) Calculate all r (m)c,v)
4) At all r (m)c,v) Finding out the residual error of v whose likelihood ratio sign can be changed and finding out the residual error
Figure FDA0002601500210000018
5) Computing
Figure FDA0002601500210000019
And
Figure FDA00026015002100000110
6) computing
Figure FDA00026015002100000111
7)I＜IthrAt all time, in
Figure FDA00026015002100000112
Finding v with changed likelihood ratio signbAnd finding out the related residual error therein
Figure FDA00026015002100000113
I＞IthrAt all time, in
Figure FDA00026015002100000114
In the process of finding
Figure FDA00026015002100000115
8) If all the check equations meet or reach the set maximum iteration number, ending the decoding, otherwise, returning to the step 5)
Wherein: m isc,vThe messages from all check nodes to variable nodes are generally referred to;
Figure FDA00026015002100000116
generalized variable node vnMessages to all connected check nodes;
Figure FDA00026015002100000117
representing variable node viA channel prior probability of (d); r (m)c,v) The residual errors before and after the update of the messages from all the check nodes to the variable nodes are generally referred to;
Figure FDA00026015002100000118
represents check node ciTo variable node vjBefore and after updating the likelihood ratio value of (a); n (v)i) Representation and variable node viAll connected check node sets, check node ca∈N(vi) Represents check node caWill take the sum of the variable node viConnecting all check nodes;
Figure FDA00026015002100000119
representing slave check node caTo variable node viThe message of (a) is received,
Figure FDA00026015002100000120
representing a slave variable node viTo check node cjThe message of (2); n (c)j) Representing and checking node cjAll variable nodes connected, N (c)j)\viRepresenting and checking node cjAll non-variable-included nodes v connectediOther variable node of vb∈N(cj)\viRepresenting variable node vbWill take and check node cjAll non-variable-included nodes v connectediOther variable nodes of (2); i denotes the number of iterations, and IthrIs an iteration number threshold;
likelihood ratio message residual calculation formula: r (m)k)＝||fk(m)-mk||∞，mkE is m; wherein m represents the calculation fk(m) required correlation messages, mkAnd fk(m) represent likelihood ratios before and after the check node to variable node update, respectively.
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