The Gelfand-Pinsker channel: Strong converse and upper bound for the reliability function

We consider a Gelfand-Pinsker discrete memoryless channel (DMC) model and provide a strong converse for its capacity. The strong converse is then used to obtain an upper bound on the reliability function. Instrumental in our proofs is a new technical lemma which provides an upper bound for the rate of codes with codewords that are conditionally typical over large message dependent subsets of a typical set of state sequences. This technical result is a nonstraightforward analog of a known result for a DMC without states that provides an upper bound on the rate of a good code with codewords of a fixed type (to be found in, for instance, the Csiszar-Kurner book).