Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical considerations such as channel uncertainty and implementation constraints rule out the use of an optimal decoder. The mismatched decoding problem addresses such scenarios by considering the case that the decoder cannot be optimized, but is instead fixed as part of the problem statement. This problem is not only of direct interest in its own right, but also has close connections with other long-standing theoretical problems in information theory. In this monograph, we survey both classical literature and recent developments on the mismatched decoding problem, with an emphasis on achievable random-coding rates for memoryless channels. We present two widely-considered achievable rates known as the generalized mutual information (GMI) and the LM rate, and overview their derivations and properties. In addition, we survey several improved rates via multi-user coding techniques, as well as recent developments and challenges in establishing upper bounds on the mismatch capacity, and an analogous mismatched encoding problem in rate-distortion theory. Throughout the monograph, we highlight a variety of applications and connections with other prominent information theory problems.

翻译：香农信道编码定理描述了在采用最优编码与解码策略时，可通过通信信道可靠传输的最大信息速率。然而在许多实际场景中，信道不确定性及实现约束等实际因素排除了使用最优解码器的可能性。失配解码问题正是针对此类场景而提出，它假定解码器无法优化，而是作为问题设定的固定组成部分。该问题不仅具有直接的研究价值，还与信息论中其他长期存在的理论问题密切相关。本专著系统回顾了失配解码问题的经典文献与最新进展，重点探讨了无记忆信道下可达的随机编码速率。我们阐述了两种被广泛研究的可达速率——广义互信息（GMI）与LM速率，并概述了其推导过程与性质。此外，我们综述了通过多用户编码技术获得的若干改进速率，以及失配容量上界建立方面的最新进展与挑战，同时讨论了率失真理论中与之对应的失配编码问题。本专著贯穿始终地强调了该课题的多种应用及其与其他重要信息论问题的内在联系。