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Research of the Soft Decision Decoding Algorithm Based on Belief Propagation

Min, Rui, HE Jian-min, He, Min, Ding, Wei

Published Jul 17, 2012• 1 citation
OpenAlex

Abstract

Low Density Parity Check(LDPC)codes is one of the high topics of the channel coding theory and has been paid more and more attention．In this paper，a modified decoding algorithm based on the belief propagation(BP) algorithm is proposed．It normalizes the variable message to compensate the simplified check message for reducing complexity. The simulation results show that the proposed algorithm can improve the BER property and reduce the computation complexity．

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中国邮电高校学报：英文版•Jan 1, 2004•1 citation
Low Density Parity Check(LDPC)codes is one of the high topics of the channel coding theory and has been paid more and more attention．In this paper，a modified decoding algorithm based on the belief propagation(BP) algorithm is proposed．It normalizes the variable message to compensate the simplified check message for reducing complexity. The simulation results show that the proposed algorithm can improve the BER property and reduce the computation complexity．
According to no-convergence of falsely oscillating iteration in the low-density parity-check(LDPC) decoding at the range from medium to high SNRs(Signal to Noise Ratios),we propose a modified LDPC belief propagation(BP) decoding algorithm,i.e.soft value zero-forcing BP algorithm.By setting extrinsic information of the oscillating iteration bit nodes into zero,the impact on the iteratively decoding from false channel information is greatly reduced.And it also improves the performance of the decoding algorithm.Furthermore,a decision criterion of oscillating iteration nodes is presented to increase the accuracy of the decision.Simulation results show that the proposed algorithm has better decoding performance than that of the BP algorithm with the same iterations at medium and high SNRs.
In this paper, we propose a belief-propagation (BP)-based decoding algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified BP-based algorithm. The normalization factors can be obtained not only by simulation, but also, importantly, theoretically. This new BP-based algorithm is much simpler to implement than BP decoding as it requires only additions of the normalized received values and is universal, i.e., the decoding is independent of the channel characteristics. Some simulation results are given, which show this new decoding approach can achieve an error performance very close to that of BP on the additive white Gaussian noise channel, especially for low-density parity check (LDPC) codes whose check sums have large weights. The principle of normalization can also be used to improve the performance of the max-log-MAP algorithm in turbo decoding, and some coding gain can be achieved if the code length is long enough.
Belief propagation (BP) algorithm is commonly used in soft decoding of Low Density Parity Check Code (LDPC). However, a significant disadvantage of this method is that the computational complexity is high in high order M-QAM modulation. This paper proposes an optimized algorithm to reduce the posterior probability calculation in soft decoding, which estimates an approximate decision point in the constellation map via channel equalization. Then a contractible constellation decision space is delimited by the approximate decision point and its surrounding points with the minimum European distance. Compared with the conventional soft decoding, simulation results show that the proposed algorithm can effectively reduce the computational complexity of BP decoding with tiny loss of the decoding accuracy. The proposed algorithm reduces nearly 96 percent of the computational complexity of posterior probability in the case of 256QAM modulation.
In this paper, we propose a new reduced-complexity decoding algorithm of Low-Density Parity-Check (LDPC) codes, called Belief-Propagation-Approximated (BPA) algorithm, which utilizes the idea of normalization and translates approximately the intricate nonlinear operation in the check nodes of the original BP algorithm to only one operation of looking up the table. The normalization factors can be obtained by simulation, or theoretically. Simulation results demonstrate that BPA algorithm exhibits fairly satisfactory bit error performance on the Additive White Gaussian Noise (AWGN) channel.
Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.
In this paper, we propose a new reduced-complexity decoding algorithm of Low-Density Parity-Check (LDPC) codes, called Belief-Propagation-Approximated (BPA) algorithm, which utilizes the idea of normaliza-tion and translates approximately the intricate nonlinear operation in the check nodes of the original BP algorithm to only one operation of looking up the table. The normalization factors can be obtained by simulation, or theoretically. Simulation results demonstrate that BPA algorithm exhibits fairly satisfactory bit error performance on the Additive White Gaussian Noise (AWGN) channel.