The question of finding a single-letter formula for the mismatch capacity, which is the supremum of achievable rates of reliable communication when the receiver uses a sub-optimal decoding rule, has been a long-standing open problem. This question has many applications in communications, Information Theory and Computer Science. For example, the zero-error capacity of a channel is a special case of mismatch capacity.
In this talk, I will give a brief overview of the problem, and introduce a new bounding technique called the “multicasting approach,” which straightforwardly yields single-letter upper bounds on the mismatch capacity of stationary memoryless channels. I will also present equivalence classes of isomorphic channel-metric pairs that share the same mismatch capacity, and a sufficient condition for the tightness of the bound for the entire equivalence class.