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We introduce a new analysis technique to derive a single-letter upper boundon the mismatch capacity of a stationary, single-user, memoryless channel witha decoding metric $q$. Our bound is obtained by considering a multicasttransmission over a two-user broadcast channel with decoding metrics $q$ and$\rho$ at the receivers, referred to as $(q,\rho)$-surely degraded. Thischannel has the property that the intersection event of correct $q$-decoding ofreceiver $1$ and erroneous $\rho$-decoding of receiver $2$ has zero probabilityfor any fixed-composition codebook of a certain composition $P$. Our boundholds in the strong converse sense of an exponential decay of the probabilityof correct decoding at rates above the bound. Further, we refine the proof andpresent a bound that is at least as tight as that of any choice of $\rho$.Several examples that demonstrate the strict improvement of our bound comparedto previous results are analyzed. Finally, we detect equivalence classes ofisomorphic channel-metric pairs $(W,q)$ that share the same mismatch capacity.We prove that if the class contains a matched pair, then our bound is tight andthe mismatch capacity of the entire class is fully characterized and is equalto the LM rate, which is achievable by random coding, and may be strictly lowerthat the matched capacity.

A Single-Letter Upper Bound on the Mismatch Capacity via Multicast Transmission