Machine learning techniques have garnered great interest in designing communication systems owing to their capacity in tacking with channel uncertainty. To provide theoretical guarantees for learning-based communication systems, some recent works analyze generalization bounds for devised methods based on the assumption of Independently and Identically Distributed (I.I.D.) channels, a condition rarely met in practical scenarios. In this paper, we drop the I.I.D. channel assumption and study an online optimization problem of learning to communicate over time-correlated channels. To address this issue, we further focus on two specific tasks: optimizing channel decoders for time-correlated fading channels and selecting optimal codebooks for time-correlated additive noise channels. For utilizing temporal dependence of considered channels to better learn communication systems, we develop two online optimization algorithms based on the optimistic online mirror descent framework. Furthermore, we provide theoretical guarantees for proposed algorithms via deriving sub-linear regret bound on the expected error probability of learned systems. Extensive simulation experiments have been conducted to validate that our presented approaches can leverage the channel correlation to achieve a lower average symbol error rate compared to baseline methods, consistent with our theoretical findings.

翻译：机器学习技术因其处理信道不确定性的能力，在设计通信系统中引起了极大兴趣。为基于学习的通信系统提供理论保证，近期一些工作基于独立同分布信道假设分析了所设计方法的泛化界，而该条件在实际场景中很少满足。本文摒弃了独立同分布信道假设，研究了在时间相关信道上学习通信的在线优化问题。针对此问题，我们进一步聚焦于两个具体任务：为时间相关衰落信道优化信道解码器，以及为时间相关加性噪声信道选择最优码本。为利用所考虑信道的时域相关性以更好地学习通信系统，我们基于乐观在线镜像下降框架开发了两种在线优化算法。此外，我们通过推导所学系统期望错误概率的次线性遗憾界，为所提算法提供了理论保证。大量仿真实验验证了所提出的方法能够利用信道相关性，相较于基线方法实现更低的平均符号错误率，这与我们的理论发现一致。