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International Conference on Computer and Communication Systems (ICCCS)

Low Complexity Construction of Polar Codes with BP Decoder over Medium to High SNR Region

Hui Wang, Shuolei Gan

Published Apr 21, 2023• 1 citation

Abstract

In this paper, we focus on the low-complexity construction method of polar codes with belief propagation (BP) decoder over additive white Gaussian noise (AWGN) channels. Firstly, the zero-noise BP decoding analysis method is proposed to determine the reliability of each bit channel via recursively calculating log-likelihood ratios (LLRs) of nodes from right to left in the factor graph. The final LLR can comprehensively reflect the structural characteristics of each bit channel. Then, the zero-noise LLR criterion based construction is introduced to select the frozen bit indices. Specifically, the lower the LLR value, the higher the priority of the corresponding bit selected as the frozen bit. Due to the assumed noise-free environment, the proposed zero-noise LLR criterion based construction is channel-independent. Finally, the simulation results show that, the zero-noise LLR criterion based construction can sort out the critical bit channels to load the frozen bits. When compared with other construction methods for BP decoder, such as the LLR-based bit-swapping construction and the simulation-based bit-swapping construction, the proposed zero-noise LLR criterion based construction not only has the best error correction ability over medium to high signal-to-noise ratio (SNR) region, but also exhibits the lowest construction complexity.

DOI: 10.1109/icccs57501.2023.10151050

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In this paper, we focus on the low-complexity construction method of polar codes with belief propagation (BP) decoder over additive white Gaussian noise (AWGN) channels. Firstly, the zero-noise BP decoding analysis method is proposed to determine the reliability of each bit channel via recursively calculating log-likelihood ratios (LLRs) of nodes from right to left in the factor graph. The final LLR can comprehensively reflect the structural characteristics of each bit channel. Then, the zero-noise LLR criterion based construction is introduced to select the frozen bit indices. Specifically, the lower the LLR value, the higher the priority of the corresponding bit selected as the frozen bit. Due to the assumed noise-free environment, the proposed zero-noise LLR criterion based construction is channel-independent. Finally, the simulation results show that, the zero-noise LLR criterion based construction can sort out the critical bit channels to load the frozen bits. When compared with other construction methods for BP decoder, such as the LLR-based bit-swapping construction and the simulation-based bit-swapping construction, the proposed zero-noise LLR criterion based construction not only has the best error correction ability over medium to high signal-to-noise ratio (SNR) region, but also exhibits the lowest construction complexity.

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This paper proposes a modified belief propagation( MBP) decoder for polar codes,in which the log-likelihood ratios( LLRs) associated with the frozen nodes would be revised by a selective correction parameter when the LLRs of frozen nodes are wrongly calculated. By using the Gaussian approximation,an appropriate parameter is obtained creatively. The principles of log-domain BP decoder and corresponding modified decoding algorithm are described in this paper. Finally,computational complexity analysis and performance simulation are given. Data results indicate that compared with the existing BP decoder,the modified BP decoder can obtain a better bit error performance of about 0. 2 dB at the cost of a little computational complexity.

Due to the design principle of parallel processing, belief propagation (BP) decoding is attractive, and it provides good error-correction performance compared with successive cancellation (SC) decoding. However, its error-correction performance is still inferior to that of successive cancellation list (SCL) decoding. Consequently, this paper proposes a novel flip-list- (FL)-enabled belief propagation (BP) method to improve the error-correction performance of BP decoding for polar codes with low computational complexity. The proposed technique identifies the vulnerable channel log-likelihood ratio (LLR) that deteriorates the BP decoding result. The FL is utilized to efficiently identify the erroneous channel LLRs and correct them for the next BP decoding attempt. The preprocessed channel LLR through FL improves the error-correction performance with minimal flipping attempts and reduces the computational complexity. The proposed technique was compared with the state-of-the-art BP, i.e., BP bit-flip (BP-BF), generalized BP-flip (GBPF), cyclic redundancy check (CRC)-aided (CA-SCL) decoding, and ordered statistic decoding (OSD), algorithms. Simulation results showed that the FL-BP had an excellent block error rate (BLER) performance gain up to 0.7 dB compared with BP, BP-BF, and GBPF decoder. Besides, the computational complexity was reduced considerably in the high signal-to-noise ratio (SNR) regime compared with the BP-BF and GBPF decoding methods.

Bit flipping was first used to improve the decoding performance of successive cancellation (SC) decoder. Since SC decoding process is serial, so the first bit that goes wrong in the decoding process will cause several subsequent bits to go wrong, which will suffer from higher decoding delay than belief propagation (BP) parallel decoding. In order to meet the performance of 5G low latency and high reliability, BP decoding algorithm have received a lot of attention. However, at medium and high signal-to-noise ratios (SNR), BP decoding does not perform as well as the SC list (SCL) decoding algorithm. Hence, BP decoding algorithm borrows bit-flip strategies from SC bit flip (SCF) decoder to improve the performance. The performance of BP bit flip (BPF) decoding depends on whether the construction of the flip set is correct, so this letter proposes a flip set construction approach based on the standard deviation of the log-likelihood ratio (LLR) and the reliability weight of polarized channels, which is comparable to the existing BPF decoding, the improved algorithm can identify the error-prone bits more efficiently and improve the decoding performance.

In order to reduce the decoding latency, a new early stopping criterion is proposed for belief propagation (BP) decoding. A kind of special processing elements (PEs) of BP decoder called frozen and information PE (FIPE) is selected to predict whether decoding is successful or not. Statistics indicate that FIPE can be considered reliable when the frozen bit is decoded successfully. The proposed criterion is based on the fact that the number of reliable FIPE increase along with iterations and the variation trend is approximate to the ratio of correct information bits. In the term of hardware complexity, the proposed method has a linear correlation with the number of FIPE. This criterion consumes only ‘xor’ and ‘or’ gates to check stopping condition. Simulation results show that the proposed criterion achieves lower latency than Worst Information Bits (WIB) and Frozen Bit Error Rate (FBER) without BLER degradation compared with fixed and G-matrix. Compared with WIB, FBER, Best Frozen Bits (BFB) criterion, the proposed criterion has the lowest hardware complexity.

Under the condition of the Additive White Gaussian Noise(AWGN) channel,both the hard and soft decision decoding algorithms suitable for LDPC codes are simulated and comparatively analyzed based on analyzing the decoding algorithm for LDPC codes.The variable message correlation for Log-Likelihood-Ratio Belief-Propagation(LLR-BP) algorithm in soft decision algorithm is decreased by introducing a multiplicative correction factor.The simulation results show that the decoding error-correction performance of the modified LLR-BP algorithm is greatly improved with little increase of computing complexity.