New Upper Bounds on the Mismatch Capacity and the Mismatched Reliability Function

We develop a novel framework for proving converse theorems for channel coding, which is based on the analysis technique of multicast transmission with an additional auxiliary receiver, which serves as a genie to the original receiver. The genie provides the original receiver a certain narrowed list of codewords to choose from that includes the transmitted one. This technique is used to derive upper bounds on the mismatch capacity of discrete memoryless channels as well as the reliability function with a mismatched decoding metric. Unlike previous works, our bounding technique exploits also the inherent symmetric requirement from the codewords, leading to these upper bounds. Since the computations of most of the known bounds on the mismatch capacity are rather complicated, we further present a method to obtain possibly looser bounds that are easier to compute. As an example, we analyze the binary-input channels case. We conclude by presenting simpler bounds on the reliability function, and provide sufficient conditions for their tightness in certain ranges of rates.