标题： 循环等变神经解码器用于循环码 显示英文标题

标题： Cyclically Equivariant Neural Decoders for Cyclic Codes

摘要： 神经解码器被引入作为经典信念传播（BP）解码算法的推广，其中BP算法中的网格图被视为神经网络，并通过训练神经网络来优化网格图中的权重。 在本工作中，我们通过利用循环码的循环不变性，提出了一种新型的神经解码器。 更具体地说，我们在神经解码器的权重上施加了一个平移不变结构，使得任何输入的循环移位都会导致输出的相同循环移位。 对BCH码和删余 Reed-Muller（RM）码的大量仿真表明，当解码循环码时，我们的新解码器始终优于之前的神经解码器。 最后，我们提出了一种列表解码过程，可以显著降低BCH码和删余RM码的解码错误概率。 对于某些高率码，我们的列表解码器与最大似然解码器之间的差距小于$0.1$dB。 代码可在 https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders 获得 显示英文摘要

摘要： 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 https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders