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Globecom

MCMC Decoding of LDPC Codes with BP Preprocessing

Jiun-Ting Huang, Young-Han Kim

Published Dec 1, 2020• 3 citations
Publisher

Abstract

Monte Carlo Markov chain (MCMC) decoding is a randomized algorithm which has been proven to be near-optimal in terms of decoding error probability. However, the exponentially slow mixing rate of Markov chains seems to preclude MCMC decoding from applications concerning even short blocklength codes. In contrast, belief propagation (BP) is a deterministic algorithm that is empirically fast but sub-optimal in error rate when it is used to decode low-density parity-check (LDPC) codes. In this paper, a code-independent BP-MCMC hybrid decoder is devised for short-blocklength LDPC codes. Theoretical error analysis of the hybrid algorithm is provided. Preliminary experiments show that the preprocessing of BP successfully reduces the time complexity of MCMC decoding and hence significantly improves the applicability of MCMC decoders to short LDPC codes.

DOI
10.1109/globecom42002.2020.9348002

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Monte Carlo Markov chain (MCMC) decoding is a randomized algorithm which has been proven to be near-optimal in terms of decoding error probability. However, the exponentially slow mixing rate of Markov chains seems to preclude MCMC decoding from applications concerning even short blocklength codes. In contrast, belief propagation (BP) is a deterministic algorithm that is empirically fast but sub-optimal in error rate when it is used to decode low-density parity-check (LDPC) codes. In this paper, a code-independent BP-MCMC hybrid decoder is devised for short-blocklength LDPC codes. Theoretical error analysis of the hybrid algorithm is provided. Preliminary experiments show that the preprocessing of BP successfully reduces the time complexity of MCMC decoding and hence significantly improves the applicability of MCMC decoders to short LDPC codes.
Low-density parity check (LDPC) codes have attracted the attention of a large number of researchers with its near-Shannon performance and easy implementation features. As a data coding scheme under the 5G scenario, how to achieve efficient encoding/decoding for LDPC codes has become one of the important research topics. Under this condition, this paper 1) proposes a novel decoding algorithm for LDPC codes using the Markov Chain Monte Carlo (MCMC) method and 2) introduces two improved versions, MCMC-S and MCMC-L, which achieve better results. Simulation figures show that the improved methods outperform the traditional belief propagation (BP) decoding method in relatively short codes by more than 1 dB at the bit error rate (BER) of 10-3. Very large scale integration (VLSI) architecture of the proposed method is also given in this paper.
In this paper, an iterative soft-decision hybrid decoding algorithm for non-binary low-density parity-check (LDPC) codes with short codeword lengths is proposed. The rationale of the approach is to combine the classical belief propagation (BP) iterative LDPC decoding algorithm with the most reliable basis (MRB) decoding algorithm. This allows to achieve significant performance improvements, with a complexity that, for medium/low error rates, is only slightly higher than that of the BP algorithm alone. The performance improvement with respect to pure BP decoding is up to 0.7 dB at codeword error rate (CER) ≈ 10-5. Notably, for a fixed MRB order, hybrid decoding achieves a gain up to 0.5 dB at CER ≈ 10-5with respect to BP decoding and MRB decoding used alone.
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.
A hybrid belief propagation (BP) decoding algorithm for low-density parity-check code is proposed to accelerate the convergence of decoding and reduce the number of decoding iterations. The hybrid scheme is presented by integrating the BP algorithm with the bit-flipping function which is used as adaptive weighted factor in the BP iteration decoding. The adaptive weighting factor is based on the average weighted reliability measure of the hard output of decoder. The proposed hybrid adaptive weighted iteration scheme can efficiently increase the convergence speed of the belief propagation decoding and therefore improve the error performance. Simulation results show that the proposed algorithm can significantly reduce the decoding complexity and achieve better error performances as compared with the sum-product algorithm.
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.