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Science China Information Sciences

Belief propagation list bit-flip decoder for polar codes

Yuyu Yang, Yaoyue Hu, Zhiwen Pan, Nan Liu, Shenjie Xia

Published Aug 18, 2021• 2 citations
Publisher
DOI
10.1007/s11432-019-2801-6

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Belief propagation list (BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL (CA-SCL) decoding. In this work, an improved segmented belief propagation list decoding based on bit flipping (SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the error-correction performance of BPL decoding for medium and long codes. It is more than 0.25 dB better than the state-of-the-art BPL decoding at a block error rate (BLER) of 10−5, and outperforms CA-SCL decoding in the low signal-to-noise (SNR) region for (1024,0.5) polar codes.

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Belief propagation list (BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL (CA-SCL) decoding. In this work, an improved segmented belief propagation list decoding based on bit flipping (SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the error-correction performance of BPL decoding for medium and long codes. It is more than 0.25 dB better than the state-of-the-art BPL decoding at a block error rate (BLER) of 10−5, and outperforms CA-SCL decoding in the low signal-to-noise (SNR) region for (1024,0.5) polar codes.
Though BP-based polar decoder has low latency, the BLER performance of it does not outperform the CA-SCL decoder with a large list size, which prevents BP-based decoder from its practical implementation. In this paper, we propose a noise-aided belief propagation list bit-flip (NA-BPLF) decoder by merging BPL with artificial noise and bit flipping. In NA-BPLF, when CA-BPL decoding fails, the error-prone bit is chosen for the bit flipping operations based on the decoding results generated by the previous CA-BPL decoding process, and then artificial noise is superimposed. Simulation results show that NA-BPLF achieves better BLER performance which is close to large list size CA-SCL decoder while still keeping the low latency.
Recently, belief propagation list (BPL) decoding has been proposed to achieve the excellent parallel decoding performance of polar codes with high throughput and low latency. However, the performance gap between BPL decoding and state-of-the-art successive cancellation list (SCL) decoding is still significant at practical SNRs. In this letter, we propose an efficient BPL flip (EBPLF) decoding algorithm for filling this gap. Firstly, an efficient bit-flipping strategy under BPL decoding is proposed to allow multiple bits being flipped more efficiently than the existing bit-flipping strategy. Then, by exploiting the decoding diversity and reliability of each bit over the multiple factor graphs within BPL decoding, an enhanced flip set is constructed to identify the error-prone patterns in an efficient way. Extensive simulation results show that EBPLF decoding outperforms the existing BPLF scheme and approaches the performance of adaptive SCL decoding at practical SNRs with much lower average latency.