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Communications technology

A Modified BP for Polar Codes

Zhang Qing-shuan

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

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.

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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.
The belief propagation (BP) algorithm for polar codes has attracted significant attention due to its soft-output property and high parallelism. However, the BP algorithm is not comparable with the successive cancellation list (SCL) algorithm in terms of the error-correction performance. In this paper, we propose a high-stage BP flip (HSBPF) algorithm to further improve the error-correction performance of the BP algorithm by analyzing the distribution of log-likelihood ratio (LLR) values. Simulation results show that the decoding latency can be reduced by 30% with the proposed algorithm. Moreover, benefiting from the simplified message passing of the factor graph, the computational complexity of the proposed algorithm is also significantly reduced compared with the existing algorithms.
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.
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.
Since the polar code was discovered by Arikan, many decoding methods have been proposed, one of which is the belief propagation (BP) decoding. Its inherent high parallel level makes it suitable for high‐speed applications. A novel BP decoder based on a modified three‐by‐three kernel matrix is proposed. The corresponding decoding algorithm and frozen bits selection method are presented. The numerical results show that it has a similar error correcting capability compared with the original polar BP decoder. More importantly, the message memory requirement can be reduced from O ( N log 2 N ) to O ( N log 3 N ), and the decoding delay can be reduced accordingly.
Belief Propagation(BP) decoders of Polar Codes can run in parallel and have a remarkable throughput achievement at a cost of performance degradation, when compared with other decoding algorithms of polar codes. The existing improved algorithms still have a gap to be optimized in performance, complexity or latency. This paper proposes a modified BP flipping algorithm by introducing random penalty items into the reliability metrics of bits to correct un-converged errors under the type of noise with Gaussian distributions considered. Simulation results illustrate that the proposed penalizing method can exhibit significant performance gains over the original BP and other three existing BP flipping decoding algorithms with different blocks in the additive white Gaussian noise channel(AWGN) under a lower decoding latency. This shows the proposed scheme identifies the error-prone bits more efficiently.
In this paper, we propose a simplified belief propagation(SBP) decoder for the polar codes, where the update calculation for the messages of the so-called frozen nodes is replaced by setting these nodes' messages by prior probabilities during the BP procedure. Numerical results show that the derived SBP yields almost the same performance as the BP decoders in the literature, while the computational complexity is reduced significantly, which make our SBP more suitable for practical application as compared to the existing BP decoders.