3 problems

Let $W$ be a discrete memoryless channel with decoding metric $q$, and let $C_{\mathrm{M}}$ denote the mismatched capacity. For each positive integer $k$, let…

Csiszár–Narayan factorization conjecture. A necessary condition for $C_{\textnormal{0-u}}=C$ is that the channel law admit such a factorization on some capacity-achieving subset of…

Attainment conjecture. In most cases, this supremum is attained, and consequently