Cyclically Equivariant Neural Decoders for Cyclic Codes

Xiangyu Chen, Min Ye
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:1771-1780, 2021.

Abstract

Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by training the neural network. In this work, we propose a novel neural decoder for cyclic codes by exploiting their cyclically invariant property. More precisely, we impose a shift invariant structure on the weights of our neural decoder so that any cyclic shift of inputs results in the same cyclic shift of outputs. Extensive simulations with BCH codes and punctured Reed-Muller (RM) codes show that our new decoder consistently outperforms previous neural decoders when decoding cyclic codes. Finally, we propose a list decoding procedure that can significantly reduce the decoding error probability for BCH codes and punctured RM codes. For certain high-rate codes, the gap between our list decoder and the Maximum Likelihood decoder is less than $0.1$dB. Code available at github.com/cyclicallyneuraldecoder

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-chen21w, title = {Cyclically Equivariant Neural Decoders for Cyclic Codes}, author = {Chen, Xiangyu and Ye, Min}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {1771--1780}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/chen21w/chen21w.pdf}, url = {https://proceedings.mlr.press/v139/chen21w.html}, abstract = {Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by training the neural network. In this work, we propose a novel neural decoder for cyclic codes by exploiting their cyclically invariant property. More precisely, we impose a shift invariant structure on the weights of our neural decoder so that any cyclic shift of inputs results in the same cyclic shift of outputs. Extensive simulations with BCH codes and punctured Reed-Muller (RM) codes show that our new decoder consistently outperforms previous neural decoders when decoding cyclic codes. Finally, we propose a list decoding procedure that can significantly reduce the decoding error probability for BCH codes and punctured RM codes. For certain high-rate codes, the gap between our list decoder and the Maximum Likelihood decoder is less than $0.1$dB. Code available at github.com/cyclicallyneuraldecoder} }
Endnote
%0 Conference Paper %T Cyclically Equivariant Neural Decoders for Cyclic Codes %A Xiangyu Chen %A Min Ye %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-chen21w %I PMLR %P 1771--1780 %U https://proceedings.mlr.press/v139/chen21w.html %V 139 %X Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by training the neural network. In this work, we propose a novel neural decoder for cyclic codes by exploiting their cyclically invariant property. More precisely, we impose a shift invariant structure on the weights of our neural decoder so that any cyclic shift of inputs results in the same cyclic shift of outputs. Extensive simulations with BCH codes and punctured Reed-Muller (RM) codes show that our new decoder consistently outperforms previous neural decoders when decoding cyclic codes. Finally, we propose a list decoding procedure that can significantly reduce the decoding error probability for BCH codes and punctured RM codes. For certain high-rate codes, the gap between our list decoder and the Maximum Likelihood decoder is less than $0.1$dB. Code available at github.com/cyclicallyneuraldecoder
APA
Chen, X. & Ye, M.. (2021). Cyclically Equivariant Neural Decoders for Cyclic Codes. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:1771-1780 Available from https://proceedings.mlr.press/v139/chen21w.html.

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