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IEEE Vehicular Technology Conference

CRC-Aided Adaptive Belief Propagation Decoding of NR LDPC Codes

Xianwen Zhang, Ming Jiang, Mingyang Zhu, Kailin Liu, Chunming Zhao

Published Jun 1, 2022• 3 citations
Publisher

Abstract

In this paper, we focus on how to further improve the performance of short block-length low-density parity-check (LDPC) codes, especially the short LDPC codes in 5th generation (5G) New Radio (NR) systems. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of partial cyclic redundancy check (CRC) bits. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoder parameters. Moreover, the proposed partial CRC-aided ABP (CA-ABP) decoding can be combined with the conventional BP decoding to further improve the performance. Simulation results show that compared with the BP decoding our proposed decoding method achieves an improvement in the error-correction performance.

DOI
10.1109/vtc2022-spring54318.2022.9860767

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Abstract In this letter, a modified message passing algorithm to prevent short cycles in the factor graph is proposed and combined with a relaxation technique to improve the performance of cyclic redundancy check aided belief propagation decoding for polar codes. Numerical results show that the proposed scheme can achieve a 0.7 dB coding gain, for the code rate of 0.5 at the block error rate of 10 −5 with a comparable average number of iterations over the pure belief propagation decoding scheme when the code block length is 1024.

Electronics Letters•Apr 22, 2021•3 citations
In this paper, we focus on how to further improve the performance of short block-length low-density parity-check (LDPC) codes, especially the short LDPC codes in 5th generation (5G) New Radio (NR) systems. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of partial cyclic redundancy check (CRC) bits. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoder parameters. Moreover, the proposed partial CRC-aided ABP (CA-ABP) decoding can be combined with the conventional BP decoding to further improve the performance. Simulation results show that compared with the BP decoding our proposed decoding method achieves an improvement in the error-correction performance.
In this paper, we propose a modified adaptive belief propagation (ABP) algorithm, which is referred to as the random ABP (R-ABP) algorithm, for decoding short channel codes adopted in the fifth generation (5G) New Radio (NR) wireless systems. Based on the cyclic redundancy check (CRC) concatenation structure of 5G channel codes, we can take partial or even all CRC bits into iterative R-ABP decoding to improve the error correction performance, while the error detection capability can still be guaranteed by the remaining CRC bits and a proposed threshold-based acceptance criterion. We call this improved R-ABP decoding the threshold-and-CRC-aided R-ABP (TCA-R-ABP) decoding. The simulation results show that our proposed TCA-R-ABP algorithm outperforms the state-of-the-art decoding algorithms for many 5G low-density parity-check (LDPC) and polar codes. Moreover, the proposed TCA-R-ABP algorithm leads to a unified decoder for LDPC and polar codes, which has the potential to be a lower-complexity decoder over the combination of the belief propagation (BP) and CRC-aided successive cancellation list (CA-SCL) decoders.
Algebraic codes such as BCH code are receiving renewed interest as their short block lengths and low/no error floors make them attractive for ultra-reliable low-latency communications (URLLC) in 5G wireless networks. This article aims at enhancing the traditional adaptive belief propagation (ABP) decoding, which is a soft-in-soft-out (SISO) decoding for high-density parity-check (HDPC) algebraic codes, such as Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem (BCH) codes, and product codes. The key idea of traditional ABP is to sparsify certain columns of the parity-check matrix corresponding to the least reliable bits with small log-likelihood-ratio (LLR) values. This sparsification strategy may not be optimal when some bits have large LLR magnitudes but wrong signs. Motivated by this observation, we propose a Perturbed ABP (P-ABP) to incorporate a small number of unstable bits with large LLRs into the sparsification operation of the parity-check matrix. In addition, we propose to apply partial layered scheduling or hybrid dynamic scheduling to further enhance the performance of P-ABP. Simulation results show that our proposed decoding algorithms lead to improved error correction performances and faster convergence rates than the prior-art ABP variants.
In modern communication systems, the concatenation of a low-density parity-check (LDPC) code with a cyclic redundancy check (CRC) code is commonly used for error correction. In this paper, we propose a low-complexity two-stage scheme for decoding these codes using their concatenation structures. In the first stage, the traditional belief propagation (BP)-based iterative algorithm with a relative small maximum number of iterations is performed for decoding the LDPC code. If an LDPC codeword is obtained in this stage, the decoding process terminates. Otherwise, the second stage of the decoding process is performed, in which the guessing random additive noise decoding (GRAND) algorithm is applied to the CRC code. A list of information sequences satisfying the CRC check is obtained, each of which is then encoded to an LDPC codeword. The most likely codeword among them is the output of the decoding approach. The simulation results indicate that the proposed two-stage decoding approach can outperform the traditional BP-based iterative algorithm with a large maximum number of iterations. Moreover, the average complexity of the proposed approach is relatively low.
Polar codes are the first class of error correcting codes that provably achieve the channel capacity at infinite code length. They were selected for use in the fifth generation of cellular mobile communications (5G). In practical scenarios such as 5G, a cyclic redundancy check (CRC) is concatenated with polar codes to improve their finite length performance. This is mostly beneficial for sequential successive-cancellation list decoders. However, for parallel iterative belief propagation (BP) decoders, CRC is only used as an early stopping criterion with incremental error-correction performance improvement. In this paper, we first propose a CRC-polar BP (CPBP) decoder by exchanging the extrinsic information between the factor graph of the polar code and that of the CRC. We then propose a neural CPBP (NCPBP) algorithm which improves the CPBP decoder by introducing trainable normalizing weights on the concatenated factor graph. Our results on a 5G polar code of length 128 show that at the frame error rate of 10-5and with a maximum of 30 iterations, the error-correction performance of CPBP and NCPBP are approximately 0.25 dB and 0.5 dB better than that of the conventional CRC-aided BP decoder, respectively, while introducing almost no latency overhead.
Belief propagation (BP) is an iterative and parallel decoding algorithm for polar code that satisfies high throughput and low latency requirements in 5G scenarios. In this work, we proposed a cyclic redundancy check aided belief propagation decoding with the box and match algorithm (CBP-BMA) to enhance the error-correction performance further. This algorithm first runs the BP decoder with early stopping criteria and then uses the soft decoded BP log-likelihood ratio (LLR) as the soft input to the box and match algorithm (BMA) decoder. The simulation results show that even if the reprocessing order of the BMA decoder is as low as one, the proposed algorithm shows a significant improvement than BP decoding. With code rate R=0.5 and code length N=128, the suggested algorithm has a gain of roughly 0.3dB at the desired bit error rate (BER) of 10–3.
Abstract In this letter, a modified message passing algorithm to prevent short cycles in the factor graph is proposed and combined with a relaxation technique to improve the performance of cyclic redundancy check aided belief propagation decoding for polar codes. Numerical results show that the proposed scheme can achieve a 0.7 dB coding gain, for the code rate of 0.5 at the block error rate of 10 −5 with a comparable average number of iterations over the pure belief propagation decoding scheme when the code block length is 1024.