New Converse Bounds on the Mismatched Reliability Function and the Mismatch Capacity Using an Auxiliary Genie Receiver
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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-aided-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 as well as the reliability function with a mismatched decoding metric of discrete memoryless channels. Unlike previous works, our bounding technique exploits also the inherent symmetric requirement from the codewords, leading to these new upper bounds which are tighter. Since the computations of most of the known bounds on the mismatch capacity are rather complicated, we further present a method to obtain relaxed bounds that are easier to compute. We conclude by presenting simpler bounds on the reliability function, and provide sufficient conditions for their tightness in certain ranges of rates.
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