Capacity of State-Dependent Channels with Non-Memoryless State Information and the Transmitter
A state-dependent channel is a channel whose transition probabilities may depend not only on the channel input but also on a state sequence, usually assumed to be generated by nature and modeled by a stochastic process. We consider a state dependent channel with a state sequence which is a stationary and ergodic process known non-causally to the transmitter, and establish a multi-letter formula for the capacity of this single-user channel. We show that among all the stationary-ergodic state sequences having the same single symbol distribution, the i.i.d. one is the worst. We quantify an upper bound on the gap between the achievable rate of a k-th order binning scheme and the capacity. We present and example in which the capacity of the channel controlled by a Markov chain state sequence is strictly higher than that of the same channel with an i.i.d. state sequence having the same stationary distribution. We conclude by demonstrating that in the setup of a cognitive channel with an interferer, one can benefit in terms of reliably transmitted rates if the interferer uses random coding schemes with memory rather than i.i.d. ones.
* Research was carried out towards the M.Sc. degree, supervised by Dr. Anelia Somekh-Baruch