The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over linear codes, but are still vulnerable to the presence of forward and feedback noise over the channel. In this paper, we develop a new family of non-linear feedback codes that greatly enhance robustness to channel noise. Our autoencoder-based architecture is designed to learn codes based on consecutive blocks of bits, which obtains de-noising advantages over bit-by-bit processing to help overcome the physical separation between the encoder and decoder over a noisy channel. Moreover, we develop a power control layer at the encoder to explicitly incorporate hardware constraints into the learning optimization, and prove that the resulting average power constraint is satisfied asymptotically. Numerical experiments demonstrate that our scheme outperforms state-of-the-art feedback codes by wide margins over practical forward and feedback noise regimes, and provide information-theoretic insights on the behavior of our non-linear codes. Moreover, we observe that, in a long blocklength regime, canonical error correction codes are still preferable to feedback codes when the feedback noise becomes high.

翻译：反馈通信编码的设计一直是一个长期悬而未决的问题。近年来，基于深度学习非线性编码方案的研究在线性码的基础上显著提升了通信的可靠性，但这些方案仍然容易受到信道上正向噪声和反馈噪声的影响。在本文中，我们开发了一类新型的非线性反馈码，极大地增强了其对信道噪声的稳健性。我们的自编码器架构旨在学习基于连续比特块的编码，这相较于逐比特处理具有去噪优势，有助于克服编码器与解码器之间因噪声信道造成的物理分离。此外，我们在编码器处设计了一个功率控制层，将硬件约束显式纳入学习优化中，并证明由此产生的平均功率约束在渐近意义下得到满足。数值实验表明，在实际正向噪声和反馈噪声环境中，我们的方案以显著优势优于现有最先进的反馈码，并为非线性码的行为提供了信息论层面的见解。同时，我们观察到，在长块长条件下，当反馈噪声较高时，经典纠错码仍比反馈码更优。