Improving the List Decoding Version of the Cyclically Equivariant Neural Decoder

TL;DR

This paper introduces an improved list decoding algorithm for cyclically equivariant neural decoders applied to BCH and punctured Reed-Muller codes, significantly reducing bit error rates and computational time while maintaining or improving frame error rates.

Contribution

The paper presents a novel list decoding method that enhances BER performance and reduces runtime for neural decoders on specific cyclic codes.

Findings

Up to 2dB BER gain over previous list decoder.

15% reduction in decoding runtime.

Maintains or improves FER performance.

Abstract

The cyclically equivariant neural decoder was recently proposed in [Chen-Ye, International Conference on Machine Learning, 2021] to decode cyclic codes. In the same paper, a list decoding procedure was also introduced for two widely used classes of cyclic codes -- BCH codes and punctured Reed-Muller (RM) codes. While the list decoding procedure significantly improves the Frame Error Rate (FER) of the cyclically equivariant neural decoder, the Bit Error Rate (BER) of the list decoding procedure is even worse than the unique decoding algorithm when the list size is small. In this paper, we propose an improved version of the list decoding algorithm for BCH codes and punctured RM codes. Our new proposal significantly reduces the BER while maintaining the same (in some cases even smaller) FER. More specifically, our new decoder provides up to $2$dB gain over the previous list decoder when measured by BER, and the running time of our new decoder is $15\%$ smaller. Code available at https://github.com/improvedlistdecoder/code