Finite blocklength coding for channels with side information at the receiver

The communication model of a memoryless channel that depends on a random state that is known at the receiver only is studied. The channel can be thought of as a set of underlying channels with a fixed state, where at each channel use one of these channels is chosen at random, and this selection is known to the receiver only. The capacity of a such channel is known, and is given by the expectation (w.r.t. the random state) of the capacity of the underlying channels. In this work we examine the finite-length characteristics of this channel, and their relation to the characteristics of the underlying channels. We derive error exponent bounds (random coding and sphere packing) for the channel and determine their relation to the corresponding bounds of the underlying channels. We also determine the channel dispersion and its relation to the dispersion of the underlying channels. We show that both in the error exponent bounds and in the dispersion case, the expectation of these quantities is too optimistic w.r.t. the actual value. Examples for such channels are discussed.