State Dependent Channels: Strong Converse and Bounds on Reliability Function

We consider an information theoretic model of a communication channel with a time-varying probability law. Specifically, our model consists of a state dependent discrete memoryless channel, in which the underlying state process is independent and identically distributed with known probability distribution, and for which the channel output at any time instant depends on the inputs and states only through their current values. For this channel, we provide a strong converse result for its capacity, explaining the structure of optimal transmission codes. Exploiting this structure, we obtain upper bounds for the reliability function when the transmitter is provided channel state information causally and noncausally. Instrumental to our proofs is a new technical result which provides an upper bound on 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 extension of an analogous result for a discrete memoryless channel without states; the latter provides a bound on the rate of a good code with codewords of a fixed composition.