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.

翻译：纠错码是物理通信层的关键组成部分，确保数据在噪声信道上的可靠传输。设计能够高效解码的最优线性分组码是主要关注点，尤其是对于短分组长度。尽管神经解码器近年来已展现出超越经典解码技术的优势，但码的神经设计仍是一个挑战。在本工作中，我们首次提出了一种二元线性分组码的编码器-解码器联合训练方法。为此，我们调整了编码设置，以支持在二阶伽罗瓦域上对码进行高效且可微的训练，从而实现端到端优化。我们还提出了一种新颖的Transformer模型，其中自注意力掩码以可微方式执行，以实现码梯度的有效反向传播。我们的结果表明：(i) 所提出的解码器在传统码上优于现有的神经解码方法；(ii) 所提出的框架生成的码优于相应的传统码；以及 (iii) 我们开发的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展现出增强的性能。