  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 new 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 relaxed bounds that
are easier to compute. As an example, we analyze the obtained bounds in 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.
