Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. While neural decoders have recently demonstrated their advantage over classical decoding techniques, the neural design of the codes remains a challenge. In this work, we propose for the first time a unified encoder-decoder training of binary linear block codes. To this end, we adapt the coding setting to support efficient and differentiable training of the code for end-to-end optimization over the order two Galois field. We also propose a novel Transformer model in which the self-attention masking is performed in a differentiable fashion for the efficient backpropagation of the code gradient. Our results show that (i) the proposed decoder outperforms existing neural decoding on conventional codes, (ii) the suggested framework generates codes that outperform the {analogous} conventional codes, and (iii) the codes we developed not only excel with our decoder but also show enhanced performance with traditional decoding techniques.

本研究首次提出了一种统一的编码-解码训练方法，用于二进制线性分组码，采用了适应性编码设置，支持针对二阶伽罗瓦域的端到端优化。我们还提出了一种新颖的Transformer模型，其中的自注意力掩码采用可微分的方式进行，以实现对码梯度的有效反向传播。实验结果表明：(i) 所提出的解码器在常规编码上优于现有的神经解码器；(ii) 所提出的框架生成的编码优于相应的常规编码；(iii) 我们开发的编码不仅在我们的解码器上表现出色，而且在传统解码技术上也表现出更好的性能。

学习线性分组纠错码