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：反馈通信信道编码的设计长期是一个未决的开放问题。近期针对非线性深度学习编码方案的研究表明，相较于线性编码，此类方案在通信可靠性方面取得了显著提升，但仍易受信道前向噪声与反馈噪声的影响。本文提出了一类新型非线性反馈编码，可显著增强对信道噪声的鲁棒性。我们设计的自编码器架构基于连续位块进行编码学习，相较于逐位处理方式可获得去噪优势，有助于克服编码器与解码器在噪声信道中的物理隔离问题。此外，我们在编码器端开发了功率控制层，将硬件约束显式纳入学习优化过程，并证明所得平均功率约束可渐近满足。数值实验表明，在实际前向与反馈噪声条件下，我们的方案以显著优势超越现有最优反馈编码，同时为理解非线性编码的行为提供了信息论层面的洞察。值得注意的是，我们观察到在长块长度场景下，当反馈噪声升高时，经典纠错码仍优于反馈编码。