ε-Capacities and Second-Order Coding Rates for Channels with General State

We consider state-dependent channels with general state available at both the encoder and the decoder. We establish the "-capacity and the optimistic "-capacity of such channels. The determination of these capacities allows us to provide a necessary and sufficient condition for the strong converse property to hold. We also provide a simpler sufficient condition on the firstand second-order statistics of the state process that ensures that the strong converse property holds. We then seek a finer characterization of these capacities in terms of second-order coding rates. The general results are supplemented by several examples including i.i.d. and Markov states and mixed channels. The proofs of the specializations of the general second-order result to the specific examples require new techniques such as multiple applications of various forms of the Berry-Esseen theorems.