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 (probably approximately correct) 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，信道模型的知识通常缺乏，因此收发机需要基于经验数据设计。本文研究了数据驱动方法，用于可靠选择解码度量和码率，以在未知离散无记忆信道（DMC）上实现可靠通信。我们的分析受PAC（可能近似正确）学习理论启发，且不依赖对DMC统计特性的任何假设。我们证明，对于有限训练集，一种简单的插件式解码度量选择算法很可能失败。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，该虚拟样本算法被用作构建学习算法的基本模块，该算法能够选择解码度量和码率，使得发射机和接收机能够以任意接近信道互信息的速率进行可靠通信。因此，我们得出结论：DMC是PAC可学习的。