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IEEE Transactions on Communications

Adaptive Belief Propagation Decoding of CRC Concatenated NR LDPC and Polar Codes

Mingyang Zhu, Ming Jiang, Chunming Zhao

Published Jun 20, 2022• 13 citations
Publisher

Abstract

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.

DOI
10.1109/tcomm.2022.3184359

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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.
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.
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.
Although iterative decoding of polar codes has recently made huge progress based on the idea of permuted factor graphs, it still suffers from a non-negligible performance degradation when compared to state-of-the-art CRC-aided successive cancellation list (CA-SCL) decoding. In this work, we show that iterative decoding of polar codes based on the belief propagation list (BPL) algorithm can approach the error-rate performance of CA-SCL decoding and, thus, can be efficiently used for decoding the standardized 5G polar codes. Rather than only utilizing the cyclic redundancy check (CRC) as a stopping condition (i.e., for error-detection), we also aim to benefit from the error-correction capabilities of the outer CRC code. For this, we develop two distinct soft-decision CRC decoding algorithms: a Bahl-Cocke-Jelinek-Raviv (BCJR)-based approach and a sum product algorithm (SPA)-based approach. Further, an optimized selection of permuted factor graphs is analyzed and shown to reduce the decoding complexity significantly. Finally, we benchmark the proposed CRC-aided belief propagation list (CA-BPL) decoding to state-of-the-art 5G polar codes under CA-SCL decoding and, thereby, showcase an error-rate performance not just close to the CA-SCL but also close to the maximum likelihood (ML) bound as estimated by ordered statistic decoding (OSD).
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.
This paper proposes a novel iterative decoder based on concatenated belief propagation (BP) for CRC-aided polar codes. Compared to the conventional BP-based decoders for polar codes, soft cancellation (SCAN) decoder can generate a log likelihood ratio (LLR) of coded bit with lower computational complexity without sacrificing the detection capability. Unfortunately, its performance is not as good as that of CRC-aided successive cancellation list decoder (SCLD) although SCAN decoder has advantage of hardware implementation. To compensate the performance gap, we exploit CRC structure for not only error detection but also error correction with the assistance of its error correction capability at a short code length by exchanging LLRs between SCAN decoder and BP decoder on the basis of CRC. Moreover, the sub-optimal criterion for selecting a parity check matrix of CRC for BP decoder is proposed. Finally, computer simulations are conducted to confirm the validity of our proposed method. The proposed method can obtain the gain of about 0.6 dB at BER=10-3compared to the native SCAN decoder without requiring huge memory size as in SCLD.
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.