Improving the List Decoding Version of the Cyclically Equivariant Neural Decoder
This work addresses a specific problem in error-correcting code decoding for communication systems, representing an incremental improvement over prior methods.
The paper tackles the issue of high Bit Error Rate (BER) in the list decoding version of the cyclically equivariant neural decoder for BCH and punctured Reed-Muller codes, proposing an improved algorithm that reduces BER by up to 2 dB while maintaining or reducing Frame Error Rate (FER) and decreasing running time by 15%.
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