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IEEE International Conference on Computer and Communications (ICCC)

The Novel Modified Weighted Bit-Flipping Decoding Algorithms for Reed-Muller Codes with Simple Scaling and SNR Adaption

Yufang Yin, Yingsong Chen

Published Dec 11, 2020• 0 citations
Publisher

Abstract

Bit-flipping (BF) algorithm has been widely employed in decoding linear block codes because of its simple implementation. We consider the most popular modified weighted bit-flipping (MWBF) algorithm and propose two novel LLR scaling based MWBF algorithms for RM (Reed-Muller) decoding. By introducing the log likelihood ratio as the scaling factor to tune the bit-based message and then approximately approaching the SNR adaption, the proposed two decoding algorithms outperform regular MWBF method with similar computational cost.

DOI
10.1109/iccc51575.2020.9344891

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We present a major improvement to the modified weighted bit flipping (MWBF) decoding algorithm for low density parity-check (LDPC) codes. We improve the flipping criterion by introducing a more efficient method for computing the reliability of the parity checks. We derive an approximate theoretical expression for the weighting factor and demonstrate its consistency with simulation results. The improved MWBF algorithm achieves a noticeable gain over the MWBF algorithm with only a modest increase in computational complexity.
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LDPC (Low Density Parity Check Codes) is a low -density puppet test code applied to channel codes. Among the existing LDPC decoding algorithms, the LLR-BP decoding arithmetic is too complicated to calculate the calculation due to the containing a large number of bilateral positive cut functions. Therefore, this article proposes a LDPC decoding algorithm that combines the Modified Weighted Bit Flipping Decoding Algorithm (MWBF) with the Logarithmic Likelihood Ratio Based Confidence Propagation Algorithm (LLR-BP). In the process of the LLR-BP decoding iteration, the introduction of the MWBF algorithm not only does it reduce the complexity of iteration and decoding, but also avoids the traditional weighted bit-flipping decoding algorithm (WBF). Excessive effects of code performance.
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve near-ML performance in practice. The main idea is to apply iterative decoding to a highly-redundant parity-check (PC) matrix that contains only the minimum-weight dual codewords as rows. As examples, we consider the peeling decoder for the binary erasure channel, linear-programming and belief propagation (BP) decoding for the binary-input additive white Gaussian noise channel, and bit-flipping and BP decoding for the binary symmetric channel. For short block lengths, it is shown that near-ML performance can indeed be achieved in many cases. We also propose a method to tailor the PC matrix to the received observation by selecting only a small fraction of useful minimum-weight PCs before decoding begins. This allows one to both improve performance and significantly reduce complexity compared to using the full set of minimum-weight PCs.