On state dependent channels with non-memoryless state information at the transmitter

We consider a state dependent channel with a state sequence which is a stationary and ergodic process known non-causally to the transmitter. We first 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 present an 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 interférer, one can benefit in terms of reliably transmitted rates if the interférer uses random coding schemes with memory rather than i.i.d. ones.