CN110086476B - LDPC code decoding method based on dynamic selection strategy with fixed message updating range - Google Patents

LDPC code decoding method based on dynamic selection strategy with fixed message updating range Download PDF

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CN110086476B
CN110086476B CN201910259262.2A CN201910259262A CN110086476B CN 110086476 B CN110086476 B CN 110086476B CN 201910259262 A CN201910259262 A CN 201910259262A CN 110086476 B CN110086476 B CN 110086476B
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刘星成
谢穗鹏
梁硕
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National Sun Yat Sen University
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    • 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
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    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
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Abstract

The invention particularly relates to an LDPC code decoding method based on a dynamic selection strategy with a fixed message updating range. Different from the traditional decoding method taking all check nodes as the updating range, the decoding method of the invention randomly selects a fixed number of check nodes to enter the updating range before updating the edge message each time, and then searches the edge message with the largest edge residual error from the check nodes in the updating range to update. The invention utilizes the decoding average iteration time estimation algorithm decoding performance, automatically sets a proper updating range by comparing the average iteration times of decoding in updating ranges of different sizes, thereby effectively inhibiting the greediness of a dynamic selection strategy, greatly reducing the searching complexity of searching the maximum edge residual error, and obtaining excellent error correction performance, convergence performance and throughput performance.

Description

LDPC code decoding method based on dynamic selection strategy with fixed message updating range
Technical Field
The invention relates to the technical field of communication, in particular to an LDPC code decoding method based on a dynamic selection strategy with a fixed message updating range.
Background
An LDPC (Low Density Parity Check code) code is a linear block code with excellent performance, and was first proposed by Gallager in 1962. However, the LDPC code has not attracted sufficient attention due to the hardware condition at the time. In 1981, Tanner proposed to use Tanner graph to describe message passing process of LDPC code, which greatly advanced the research process of LDPC code. In 1995, MacKey redetects the LDPC code, and comprehensively explains the performance, a construction method, an encoding method, a decoding method and the like of the code again. Since then, LDPC codes have attracted a wide range of attention. LDPC codes have excellent performance approaching the shannon limit, mainly thanks to their own characteristic sparsity. The sparsity of the LDPC code means that elements which are not 0 in a check matrix H of the LDPC code are very few, so that the correlation between messages is very low, and the reliability of message transmission is greatly improved. At present, LDPC codes have been widely used in the fields of wireless communication, ocean exploration, optical communication, digital video broadcasting, and the like. In 2016, 10 months, LDPC codes are adopted by 3GPP as coding schemes for data channels in the 5G communication standard. In the future, with the continuous and deep research and the continuous progress of coding technology, the LDPC code will play a more important role in the communication field.
The decoding updating method of the LDPC code is mainly divided into hard decision decoding and soft decision decoding. The hard decision decoding algorithm has the advantages of low decoding complexity, easy hardware implementation and the like, but the error correction performance is far inferior to that of the soft decision decoding algorithm. Soft decision decoding algorithms can be divided into three categories according to message update strategies: parallel scheduling, serial scheduling, and dynamic scheduling. Unlike parallel scheduling and serial scheduling of fixed update orders, dynamic scheduling can dynamically select an appropriate update order based on the current decoding state. Therefore, compared with parallel scheduling and serial scheduling, the dynamic scheduling has the advantages of higher convergence rate and better error correction performance, and is very suitable for high-reliability low-delay decoding scenes. In 2007, a.i.casado et al proposed a dynamic scheduling decoding algorithm based on side residual, i.e. RBP algorithm. The RBP algorithm is the most primitive dynamic scheduling decoding algorithm. In the BRP algorithm, the edge residual is equal to the absolute value of the difference between the pre-updated edge message and the current edge message. The RBP algorithm selects the edge message with the maximum edge residual error for updating each time, and the error correction performance is improved. However, the convergence performance of the RBP algorithm is general subject to the greediness of the dynamic scheduling strategy. In order to reduce greediness of the algorithm, an A.I.Casado proposes an NWRBP algorithm on the basis of an RBP algorithm. In 2013, H.C.Lee et al propose a dynamic scheduling decoding algorithm based on an updated quota, namely a Q-RBP algorithm. The Q-RBP algorithm inhibits greediness of a dynamic strategy by reasonably controlling the updating times of the edge messages, and improves error correction performance and convergence performance. In 2015, the OV-RBP algorithm based on oscillating variable node message residuals is proposed by x.c. liu et al. The OV-RBP algorithm improves the reliability of message transmission by preferentially updating the unreliable variable nodes, and obtains good error correction performance and convergence performance. However, how to suppress the greediness of the dynamic policy and further improve the decoding performance is still a problem worth of continuous research.
The greediness of LDPC code dynamic decoding algorithms are caused by the update propagation trend. After the edge with the largest edge residual is updated, the edge adjacent to the edge generates a large edge residual, so that the adjacent edges are selected to be updated in the subsequent decoding process with a high probability, thereby forming an update transmission trend. Thousands of loops exist in the LDPC code, so that the update transfer trend is easy to propagate along the edge loop on the loop, and finally, a small part of loops occupy a large amount of operation resources, and a greedy problem is formed.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an LDPC code decoding method based on a dynamic selection strategy with a fixed message updating range. According to the decoding updating method, the number of the inner rings in the range is greatly reduced by reasonably setting the updating range, the propagation of the updating transmission trend is effectively inhibited, the searching complexity of searching the maximum edge residual error is also greatly reduced, the reliability of message transmission is ensured, and the error correction performance and the throughput performance are greatly improved.
In view of the above technical problems, the present invention is to solve the following problems:
an LDPC code decoding method based on a dynamic selection strategy with a fixed message updating range comprises the following steps:
s1, setting the size n of an updating rangep: initializing n p1, in size npThe updating process of decoding n test frames is as described in S2 and S3, and the new average iteration number is calculated; if the new average iteration number is greater than the old average iteration number, the size n of the update rangepIs decreased by 1 and n is setpS1 is ended as the fixed size of the update range; otherwise, the size n of the update rangepAdding 1 to the value of (3), replacing the value of the old average iteration times with the value of the new average iteration times, and repeating S1;
s2, emptying the current updating range, and randomly selecting npThe check node enters the current updating range and executes S3;
s3, searching a C2V side message with the largest side residual error from all check nodes in the current updating range, and updating the message, wherein the C2V side message is a message transmitted to the variable node by the check node; and after the message is updated, carrying out decoding judgment. If the decoding judgment is successful or the maximum iteration times are reached, ending the decoding; if the decoding decision is unsuccessful and the maximum iteration number is not reached, skipping to execute S2 and continuing decoding.
The invention firstly estimates the decoding performance of the algorithm by using the average iteration times of decoding, and selects the range value with the best decoding performance as the fixed size of the updating range. The update range size n is setpThen, the decoding algorithm followsMachine selection npAnd (4) enabling each check node to enter an updating range, and searching the edge with the maximum edge residual error from the updating range to finish a message updating and transmitting process. If the decoding does not meet the stop criterion, clearing the updating range and then randomly selecting n againpAnd the check node enters the updating range to continue updating. The decoding algorithm is different from the conventional dynamic scheduling decoding algorithm which takes all check nodes as the updating range, and the decoding algorithm greatly reduces the number of rings formed in the updating range by randomly selecting a small number of check nodes as the updating range, thereby effectively inhibiting the greediness of the dynamic scheduling strategy and improving the decoding performance.
Further, by comparing the average iteration number of the algorithm decoding under the update ranges of different sizes, the most suitable update range size is selected, and step S1 includes the following steps:
s11, initializing the size n of the update range p1, the size of the update range, i.e. the number of check nodes contained in the update range; initializing a new average number of iterations InewOld average number of iterations I ═ 0old＝ImaxIn which ImaxThe maximum iteration number preset for the decoding updating method;
s12, in the size of npThe decoding updating process is as described in S2 and S3, the decoding iteration number used by each frame decoding is recorded, and the new average iteration number I is calculatednew；
S13, comparing the new average iteration times InewAnd old average number of iterations IoldSize of (A), if Inew>IoldThen update the range npIs decreased by 1 and n is setpEnding the update range size setting procedure as a fixed size of the update range; otherwise, the range n is updatedp Adding 1 to the value of (1) to (I)old＝InewThe jump is performed at S12, and decoding is continued.
Further, according to the monte carlo simulation test, the difference between the average iteration number calculated when n is 2000 and the average iteration number calculated when n is 10000 is less than or equal to 0.01, and the error is within a proper range, so that n can be set to 2000, assume by IiRepresenting the number of iterations used to decode the ith frame, the new average number of iterations InewCalculating by using the formula (1);
Figure BDA0002014758520000041
further, in step S3, the C2V edge message with the largest edge residual is found from all check nodes in the current update range, and the specific step of updating the message includes:
s31, searching for the C2V edge with the largest edge residual error from all check nodes in the current updating range, wherein the check node CiTo variable node vjEdge residual of
Figure BDA0002014758520000042
For precalculating C2V side information value
Figure BDA0002014758520000043
And current C2V side information value
Figure BDA0002014758520000044
The absolute value of the difference value of (a) is calculated according to the formula (2);
Figure BDA0002014758520000045
s32, assuming a check node ciTo variable node vjEdge residual of
Figure BDA0002014758520000046
If the edge residual is the maximum edge residual, the check node c is updatediTo variable node vjCurrent C2V side information value
Figure BDA0002014758520000047
Updating is performed according to the formula (3), wherein N (c)i)\vjIndicating node v except for variablejAll but check nodes ciConnected variable nodes，
Figure BDA0002014758520000048
Representing variable node vbTo check node ciV2C side information of (a);
Figure BDA0002014758520000049
s33, check node ciTo variable node vjC2V side information of
Figure BDA00020147585200000410
After the updating is finished, the variable node v is updatedjLLR value of L (v)j) Wherein the variable node vjLLR value of L (v)j) The updating is carried out according to the formula (4),
Figure BDA00020147585200000411
representing variable node vjOf the channel original information, M (v)j) Representing all and variable nodes vjConnected check nodes;
Figure BDA00020147585200000412
further, after the message is updated in step S3, a decoding decision is made, if the decoding decision is successful or reaches the maximum iteration number, the decoding is ended, if the decoding decision is unsuccessful and does not reach the maximum iteration number, the step S2 is skipped to perform, and the specific step of continuing the decoding includes:
s34. variable node vjLog-Likelihood Ratio LLR (Log-likehood Ratio) value L (v)j) After the updating is finished, decoding judgment is carried out, and if the decoding judgment is successful or the maximum iteration times are reached, decoding is quitted; if the decoding judgment is unsuccessful and the maximum iteration times are not reached, updating the variable node v according to the formula (5)jTo check node caV2C side information of (g), where M (V)j)\caIndicating the exception of check node caExcept that all and variable nodes vjConnected to each otherChecking nodes;
Figure BDA0002014758520000051
s35, for all check nodes ca∈M(vj)\ciThe C2V side information is pre-calculated using equation (3), and then the side residual is calculated using equation (2) for the next round of update iteration.
Compared with the prior art, the invention has the beneficial effects that:
in the conventional dynamic scheduling decoding algorithm, all check nodes are used as an update range, and an edge with the largest edge residual error is searched from the update range for updating. However, all the rings are also included in the update range, so that the update transmission trend is easily propagated circularly on part of the rings, and a small part of the rings occupy too many update opportunities, thereby forming the greedy of the dynamic scheduling decoding algorithm. The method is different from the conventional dynamic scheduling decoding algorithm which takes all check nodes as the updating range, and only a small number of check nodes are selected as the updating range for each updating. By selecting decoding within a smaller updating range, the invention reduces the number of rings formed within the updating range, thereby effectively inhibiting the propagation of the updating transmission trend and avoiding the generation of greedy problem of the dynamic decoding algorithm. Moreover, by decoding in a smaller updating range, the invention also reduces the searching operation required for searching the maximum edge residual error and greatly reduces the decoding complexity. Through the steps, the greedy problem of the dynamic scheduling decoding algorithm is effectively inhibited, reliable information can be more effectively transmitted, and excellent error correction performance, throughput performance and convergence performance are obtained.
Drawings
FIG. 1 is a flow chart of the algorithm of the present invention;
FIG. 2 is a flowchart illustrating the decoding update according to the present invention;
FIG. 3 is a comparison of error correction performance of 1/2- (576,288) LDPC codes;
FIG. 4 is a comparison of throughput performance of 1/2- (576,288) LDPC codes;
FIG. 5 is a comparison of the convergence performance of 1/2- (576,288) LDPC code at a signal-to-noise ratio of 3.0 dB.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Example 1
RCP (Decoding algorithm based on random select of check nodes with a predefined update range, that is, a belief propagation Decoding method based on message update range fixation) represents the abbreviation of the method of the present invention.
According to the general flow chart of the RCP decoding algorithm shown in fig. 1 and in combination with the decoding update flow chart shown in fig. 2, the specific steps of the RCP decoding algorithm are as follows:
s101, setting the size n of an updating rangep. The method comprises the following specific steps:
s1011, initializing the size n of the update rangepNew average number of iterations I ═ 1newOld average number of iterations I ═ 0old＝ImaxIn which ImaxThe maximum iteration number preset for the decoding updating method;
s1012. in the size of npThe test frames of 2000 frames are decoded under the updating range of (1), the decoding iteration number used for decoding each frame is recorded, the decoding updating process is as described in steps S102 and S103, and the new average iteration number I is calculated by using the formula (1)new. In the monte carlo simulation test, the difference between the average iteration number calculated when n is 2000 and the average iteration number calculated when n is 10000 is less than or equal to 0.01, and the error is in a proper range, so that n can be set to 2000.
The formula (1) is:
Figure BDA0002014758520000061
in the above step, the range n is updatedPInitially set to 1, i.e., decoding within a size 1 update range, then increasing the update range to 2, decoding within a size 2 update range, and so on. Average number of iterations as the update range increasesThe number will decrease and then increase. The algorithm adjusts the range according to the average iteration number, and finally selects the size n of the updating range with the minimum average iteration numberpAs a fixed size. The size of the update range is also the number of check nodes contained within the range.
S1013, comparing the new average iteration times InewAnd old average number of iterations IoldSize of (A), if Inew>IoldIf so, update the range size npIs decreased by 1 and n is setpAs a fixed size of the update range, ending the update range setting operation; otherwise, update the range size npAdding 1 to the value of (1) to (I)old＝InewThe jump is performed in S1012 to continue the comparison of the next update range.
S102, emptying the current updating range, and randomly selecting npThe check nodes enter the updating range, and step S103 is executed;
s103, updating the edge with the maximum edge residual error in the updating range, finishing a message updating process, and judging whether a stopping criterion is met after updating; if the stop criterion is met, stopping decoding; if the stop criterion is not satisfied, the skip is executed to S102, and the decoding is continued. The method comprises the following specific steps:
s1031, from all check nodes in the current updating range, searching the residual error with the maximum edge according to the formula (2)
Figure BDA0002014758520000071
C2V edge message
Figure BDA0002014758520000072
The formula (2) is:
Figure BDA0002014758520000073
s1032, updating check node ciTo variable node vjC2V side information of
Figure BDA0002014758520000074
Updating calculation is carried out according to the following formula (3):
Figure BDA0002014758520000075
s1033, variable node v is updatedjLog likelihood ratio LLR values L (v)j) Updating calculation is carried out according to the following formula (4):
Figure BDA0002014758520000076
s1034, decoding judgment is carried out on the decoding result, if the decoding judgment is successful or the maximum iteration number is reached, the stop criterion is met, and decoding is quitted; if the decoding judgment is unsuccessful and the maximum iteration times are not reached, the stopping criterion is not met, and the variable node v is updated according to the formula (5)jTo check node caV2C side information of
Figure BDA0002014758520000077
Wherein c isa∈M(vj)\ci；
S1035 is to check node ca∈M(vj)\ciPre-computing C2V side information using equation (3)
Figure BDA0002014758520000078
Computing edge residual using equation (2)
Figure BDA0002014758520000079
For the next message update procedure, wherein; v. ofb∈N(ca)\vj(ii) a And skipping and executing S102 until the decoding is successful or the maximum iteration number is reached, and ending the specific steps of the decoding method provided by the invention.
In order to compare the performance of the belief propagation decoding method based on the fixed message update range, the present embodiment performs computer simulation. Specifically, the LDPC codes are generated randomly and transmitted on AWGN channel, and various different decoding methods including the algorithm are utilizedDecoding by the algorithm, setting the maximum iteration number as 5, the maximum error frame number as 100 frames, the modulation mode as BPSK, Eb/N0Representing the normalized signal-to-noise ratio in decibels (dB).
As shown in fig. 3, a graph illustrating the error correction performance of (576,288) binary LDPC codes on AWGN channel using various decoding algorithms is shown. It can be seen from the figure that, under a low signal-to-noise ratio, such as 1.0dB to 2.0dB, the error correction performance curves of the dynamic scheduling decoding algorithms almost coincide, that is, the error correction performance difference of the algorithms is small. However, the error correction performance of each algorithm changed significantly after 2.0 dB. Before 2.0dB, the performance curves of the Q-RBP algorithm, the OV-RBP algorithm and the RCP algorithm almost coincide, but the descending speeds of the Q-RBP algorithm, the OV-RBP algorithm and the RCP algorithm are obviously higher than those of other algorithms. From 2.5dB, along with the increase of the signal-to-noise ratio, compared with the OVRBP algorithm and the Q-RBP algorithm, the RCP algorithm gradually shows advantages and becomes the algorithm with the best decoding performance. When frame error rate FER is 1.0 × 10-5And compared with the OVRBP algorithm, the RCP algorithm has about 0.13dB performance improvement.
As shown in fig. 4, a graph of throughput performance of (576,288) binary LDPC codes over AWGN channels using various different dynamic scheduling decoding algorithms is shown. Throughput (Throughput) refers to the number of frames per second (frames/s) successfully decoded by the decoding algorithm. It can be seen from the figure that at a lower signal-to-noise ratio, such as 1.0dB to 1.5dB, the performance curves of the previous dynamic scheduling decoding algorithms almost coincide, while the RCP algorithm already exhibits a significant throughput advantage. The throughput performance of each algorithm is slowly increased after 2.0dB, and the throughput performance of the RCP algorithm is rapidly improved to become the algorithm with the best throughput performance. This is because the conventional dynamic scheduling decoding algorithm using all check nodes as update ranges is easily trapped in a greedy state, and affects decoding performance. In addition, the conventional dynamic scheduling decoding algorithm searches the maximum edge residual from all check nodes, which results in high search complexity. And RCP only searches in a small number of check nodes, so that the search complexity is greatly reduced, and the throughput performance is improved. At a signal-to-noise ratio of 3.5dB, it can be seen that the throughput of the RCP algorithm is twice as much as that of the RBP algorithm, exhibiting very excellent throughput performance.
As shown in FIG. 5, it shows (576,288) a graph comparing The convergence performance of each decoding algorithm with The Number of Iterations (The Number of Iterations) at a fixed signal-to-noise ratio of 3.0dB for a regular binary LDPC code. As can be seen from fig. 5, the RCP algorithm of the present invention exhibits good convergence performance, and compared with other decoding algorithms, a lower BER (Bit Error Ratio) value is reached after the first iteration, and a relatively good convergence trend is maintained after that. After 10 iterations, the BER performance of each decoding algorithm tends to be stable, while the BER performance of the RCP algorithm is still continuously improved. The BER performance of the RCP algorithm is obviously better than that of other algorithms in 50 iterations, which shows that the RCP algorithm has better convergence performance compared with other algorithms.
In the above example simulation, the Q-RBP algorithm can refer to the following documents: H.C.Lee, Y.L.Ueng, S.M.Yeh, and W.Y.Weng.two expressed dynamic scheduling protocols for iterative LDPC decoders [ J ]. IEEE Transactions on Communications, Mar.2013,61(3): 886-.
The OV-RBP algorithm can be referred to the following documents: liu, Y.Zhang, and R.Cui.variable-node-based dynamic scheduling for belief-propagation decoding of LDPC codes [ J ]. IEEE communications.letters, Feb.2015,19(2): 147-.

Claims (4)

1. An LDPC code decoding method based on a dynamic selection strategy with a fixed message updating range is characterized by comprising the following steps:
s1, setting the size n of an updating rangep: initializing np1, in size npThe decoding updating process is as described in S2, S3, and the new average iteration number is calculated, assuming that I is usediRepresenting the number of iterations used to decode the ith frame, the new average number of iterations InewCalculated using equation (1):
Figure FDA0002694643020000011
if the new average iteration number is larger than the old average iteration number, the updating range size npIs decreased by 1 and n is setpS1 is ended as the fixed size of the update range; otherwise, update the range size npAdding 1 to the value of (3), replacing the value of the old average iteration times with the value of the new average iteration times, and repeating S1; the size of the update range, i.e. the number of check nodes contained in the update range, the old average number of iterations Iold＝ImaxIn which ImaxIs a preset maximum iteration number;
s2, emptying the current updating range, and randomly selecting npThe check node enters the current updating range and executes S3;
s3, searching a C2V side message with the largest side residual error from all check nodes in the current updating range, and updating the message, wherein the C2V side message is a message transmitted to the variable node by the check node; after the message is updated, decoding judgment is carried out; if the decoding judgment is successful or the maximum iteration times are reached, ending the decoding; if the decoding decision is unsuccessful and the maximum iteration number is not reached, skipping to execute S2 and continuing decoding.
2. The LDPC code decoding method based on the dynamic selection strategy with fixed message update range according to claim 1, wherein the step S1 comprises the following steps:
s11, setting the size n of the updating rangep: initializing the size n of the update Rangep1 is ═ 1; initializing a new average number of iterations Inew＝0；
S12, in the size of npThe decoding updating process is as described in S2, S3, the number of decoding iterations used for decoding each frame is recorded, and the new average number of iterations I is calculatednew；
S13, comparing the new average iteration times InewAnd old average number of iterations IoldSize of (A), if Inew>IoldIf so, update the range size npIs decreased by 1 and n is setpEnding the update range size setting procedure as a fixed size of the update range;otherwise, update the range size npAdding 1 to the value of (1) to (I)old＝InewThe jump is performed at S12, and decoding is continued.
3. The LDPC code decoding method based on the dynamic selection strategy with the fixed message update range according to any one of claims 1-2, wherein the C2V side message with the largest side residual is found from all check nodes in the current update range in step S3, and the specific step of performing the message update comprises:
s31, searching for the C2V edge message with the largest edge residual error from all check nodes in the current updating range, wherein the check node CiTo variable node vjEdge residual of
Figure FDA0002694643020000021
For precalculating C2V side information value
Figure FDA0002694643020000022
And current C2V side information value
Figure FDA0002694643020000023
The absolute value of the difference value of (a) is calculated according to the formula (2);
Figure FDA0002694643020000024
s32, assuming a check node ciTo variable node vjEdge residual of
Figure FDA0002694643020000025
If the edge residual is the maximum edge residual, the check node c is updatediTo variable node vjCurrent C2V side information value
Figure FDA0002694643020000026
Updating is performed according to the formula (3), wherein N (c)i)\vjIndicating node v except for variablejAll but check nodes ciThe nodes of the variables that are connected to each other,
Figure FDA0002694643020000027
representing variable node vbTo check node ciV2C side information of (a);
Figure FDA0002694643020000028
s33, check node ciTo variable node vjC2V side information of
Figure FDA0002694643020000029
After the updating is finished, the variable node v is updatedjLog likelihood ratio LLR values L (v)j) Wherein the variable node vjLLR value of L (v)j) The updating is carried out according to the formula (4),
Figure FDA00026946430200000210
representing variable node vjOf the channel original information, M (v)j) Representing all and variable nodes vjConnected check nodes;
Figure FDA00026946430200000211
4. the LDPC code decoding method based on the dynamic selection strategy with the fixed message updating range according to claim 3, wherein after the message updating in step S3 is completed, a decoding decision is made, if the decoding decision is successful or reaches the maximum iteration number, the decoding is ended, if the decoding decision is unsuccessful and does not reach the maximum iteration number, the execution of S2 is skipped, and the specific steps of continuing the decoding include:
s34. variable node vjLLR value of L (v)j) After the updating is finished, decoding judgment is carried out, and if the decoding judgment is successful or the maximum iteration times are reached, decoding is quitted; if it is translatedIf the code decision is unsuccessful and the maximum iteration times are not reached, updating the variable node v according to the formula (5)jTo check node caV2C side information of
Figure FDA00026946430200000212
Wherein M (v)j)\caIndicating the exception of check node caExcept that all and variable nodes vjConnected check nodes;
Figure FDA0002694643020000031
s35, for all check nodes ca∈M(vj)\ciThe C2V side information is pre-calculated using equation (3), and then the side residual is calculated using equation (2) for the next round of update iteration.
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