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International Journal of Communication Systems

A high‐performance belief propagation decoding algorithm for codes with short cycles

Ali Karimi-lenji, Monireh Houshmand, Fahimeh Zarmehi

Published Feb 28, 2017• 2 citations
Publisher

Abstract

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.

DOI
10.1002/dac.3275

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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.
Belief propagation (BP) decoding has been recognized for its capacity-approaching performance and high throughput when decoding long low-density parity-check (LDPC) codes. However, the application of BP decoding for short codes is hindered by dense parity-check matrices (PCMs) and prevalent short cycles in the Tanner graph. In this paper, we introduce a general method to extract an optimized sparse PCM for short binary block codes, which removes length-four cycles and enhances the connectivity of short cycles to enable BP decoding with improved performance. Notably, for short binary codes with lengths up to 64, our BP decoding performance approaches the maximum likelihood bound and surpasses the best-reported BP results with reduced computational complexity. Compared with other universal decoding algorithms, BP decoding using our extracted sparse PCMs is competitive in terms of both error-rate performance and computational complexity. These promising results suggest that our method to improve BP decoding for short codes is a step toward a practical universal BP decoder for next-generation communication systems.
In this study, an efficient decoding algorithm is proposed to decode non‐binary low‐density parity‐check (LDPC) codes. The algorithm is derived from the belief‐propagation (BP) decoding with genetic algorithm of binary LDPC codes. For the proposed algorithm, two decoding constraints are introduced to determine variable nodes which are considered highly reliable. The messages from these highly reliable variable nodes are then magnified with an appropriate parameter γ . This process can make the messages propagate in the Tanner graph more efficiently. Simulation results show that, compared with the fast Fourier transform‐based BP algorithm, the proposed algorithm can have an equal or better performance in low bit‐error‐rate region over both the additive white Gaussian noise channels and the mobile fading channels.
Low-Density Parity-Check (LDPC) codes are one of the most popular codes used in nowadays’ communication due to their high coding efficiency at low decoding complexity. With these characteristics, LDPC codes are suitable for high-speed information transmission systems. The widely used decoding algorithm for LDPC codes is Belief Propagation (BP) decoding with which the performance of LDPC codes can approach the Shannon limit. With the development of 5G, a lot of attention is given to the so-called ultra-reliable low latency communication scenario which needs the short code to transmit. However, short codes will not have a very good performance with BP decoding. To solve this problem, investigations have been done such as multiple-bases BP decoding. Although this decoding method has a better performance than BP decoding, it will cause a high complexity in the hardware implementation. Besides, an investigation on the stochastic decoding for shortcodes was proposed in 2003. This decoding method is hardware friendly, but its performance can only approach BP decoding. Inspired by multiple-bases BP decoding and stochastic decoding, binary stochastic decoding with parallel decoders is proposed in this thesis firstly. It represents stochastic sequences with multiple parallel Tanner graphs and uses hard-decision decoding in the iterative part because of the binary input bits. However, this decoding method has a severe performance loss compared to BP decoding. To avoid this problem, the enhancement method is used to make the binary sequences be non-binary sequences that can form more powerful parallel decoders. Then the non-binary symbols of these new sequences are transformed to their corresponding log-likelihood ratio which enables the iterative part to use BP decoding. In addition, combining with the ML decision of list decoding, the decision part of our stochastic decoder can fully utilize the output to increase the efficiency of the decoding method. After ensuring the performance of our non-binary stochastic decoding to be better than BP decoding, the complexity of the decoder is reduced to save the computational resources. Finally, with constant adjustments, the bit width of each non-binary symbol is determined to be 15, and the sequence length is reduced to 20 which can let the non-binary stochastic decoding has an acceptable complexity while keeping good performance.
BP decoding algorithm is one of the commonly used decoding algorithms for LDPC codes. To adapt LDPC codes to different 5G scenarios and further improve the decoding performance of short LDPC codes, a scheme combining model-driven deep learning with a traditional BP decoding algorithm is proposed. With the advantages of model-driven, this solution expands the decoding iteration process between the check node and the variable node into a neural network and proposes a parameter normalization optimization solution to solve the problem of the program with many training parameters, the edge weights of the optimized Tanner graph are re-assigned and bound. Simulation results show that the proposed scheme can improve the decoding performance of LDPC codes with short lengths.
Variant belief propagation (BP) algorithms are applied to low-density parity-check (LDPC) codes. However, conventional decoders suffer from a large resource consumption due to gathering messages from all the neighbour variable-nodes and/or check-nodes through cumulative calculations. In this paper, a check-belief propagation (CBP) decoding algorithm is proposed. Check-belief is used as the probability that the corresponding parity-check is satisfied. All check-beliefs are iteratively enlarged in a sequential recursive order, and successful decoding will be achieved after the check-beliefs are all big enough. Compared to previous algorithms employing a large number of cumulative calculations to gather all the neighbour messages, CBP decoding can renew each check-belief by propagating it from one check-node to another through only one variable-node, resulting in a low complexity decoding with no cumulative calculations. The simulation results and analyses show that the CBP algorithm provides little error-rate performance loss in contrast with the previous BP algorithms, but consumes much fewer calculations and memories than them. It earns a big benefit in terms of complexity.