In practical communication systems, knowledge of channel models is often absent, and consequently, transceivers need be designed based on empirical data. In this work, we study data-driven approaches to reliably choosing decoding metrics and code rates that facilitate reliable communication over unknown discrete memoryless channels (DMCs). Our analysis is inspired by the PAC learning theory and does not rely on any assumptions on the statistical characteristics of DMCs. We show that a naive plug-in algorithm for choosing decoding metrics is likely to fail for finite training sets. We propose an alternative algorithm called the virtual sample algorithm and establish a non-asymptotic lower bound on its performance. The virtual sample algorithm is then used as a building block for constructing a learning algorithm that chooses a decoding metric and a code rate using which a transmitter and a receiver can reliably communicate at a rate arbitrarily close to the channel mutual information. Therefore, we conclude that DMCs are PAC learnable.

翻译：在实际通信系统中，信道模型往往未知，因此收发机需要基于经验数据进行设计。本研究探讨了数据驱动方法，旨在可靠选择解码度量与码率，以实现未知离散无记忆信道（DMC）上的可靠通信。我们的分析受PAC学习理论启发，且不依赖于DMC统计特性的任何假设。研究表明，用于选择解码度量的朴素插入算法在有限训练集条件下可能失效。我们提出了一种替代算法——虚拟样本算法，并建立了其性能的非渐近下界。随后，以该算法为基本模块，构建了一个学习算法，可选择解码度量与码率，使得发射机与接收机能以任意接近信道互信息的速率实现可靠通信。由此得出结论：DMC是PAC可学习的。