Robust Multicasting and an Upper Bound on the Mismatch Capacity of the DMC

We revisit the multicasting approach to the analysis of converse bounds that we recently introduced, and present a refined proof technique for upper bounding the mismatch capacity of the DMC P
Y|X
with decoding metric q. To this end, we present an algorithm, which given a 2-user broadcast channel P
Y Z|X
, decoding metrics (q, p), and rate-
$R$
codebook, produces a sub-codebook of possibly lower rate R’, which has the property that the intersecting event of erroneous p-decoding by the
$Z$
receiver and correct q-decoding of the
$Y$
receiver has a vanishing probability. This results in a bound on the mismatch capacity of the channel to the Y-receiver that is given in terms of the sum of an achievable rate for a
$Z$
receiver of any broadcast channel having marginal P
Y|X
plus the corresponding rate reduction R - R'. We further detect the p* metric which yields the tightest bound out of all the type-dependent metrics, and focusing on the case of zero rate reduction, we show that the resulting bound is at least as tight as our previous best known upper bound [1]. We conclude by presenting sufficient conditions for the tightness of our bound and equivalence classes of code composition-channel-metric triplets.