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Canadian Journal of Electrical and Computer Engineering

Particle Swarm Optimization-Aided Enhanced Belief Propagation Bit-Flipping Decoding of Polar Codes

Guiping Li, Wen­hua Zhao, Jiaqi Liu

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1109/icjece.2026.3713262

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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.
Known for their capacity-achieving abilities, polar codes have been selected as the control channel coding scheme for 5G communications. To satisfy high throughput and low latency, belief propagation (BP) is ideal as the decoding algorithm due to its nature of parallel processing. However, the error performance of BP is in general worse than that of enhanced successive cancellation (SC). Recently, bit-flipping (BF) mechanism is applied to BP decoding to lower the error rate. However, its trial-and-error process results in longer latency. In this work, we propose a convolutional neural network-aided bit-flipping (CNN-BF) mechanism to further enhance BP decoding. With carefully designed input data and model architecture, our proposed CNN-BF can achieve better error correction capability with less flipping attempts than prior works. It also achieves a lower block error rate (BLER) than SC list (SCL).
We propose a generalization belief propagation (BP) decoding algorithm based on particle swarm optimization (PSO) to improve the performance of the polar codes. Through the analysis of the existing BP decoding algorithm, we first introduce a probability modifying factor to each node of the BP decoder, so as to enhance the error correcting capacity of the decoding. Then, we generalize the BP decoding algorithm based on these modifying factors and drive the probability update equations for the proposed decoding. Based on the new probability update equations, we show the intrinsic relationship of the existing decoding algorithms. Finally, in order to achieve the best performance, we formulate an optimization problem to find the optimal probability modifying factors for the proposed decoding algorithm. Furthermore, a method based on the modified PSO algorithm is also introduced to solve that optimization problem. Numerical results show that the proposed generalization BP decoding algorithm achieves better performance than that of the existing BP decoding, which suggests the effectiveness of the proposed decoding algorithm.