Transmission of a slowly varying Markov signal over memoryless channels

Information rates in certain discrete-time, memoryless, stationary channels with additive non-Gaussian noise and slowly varying input signal are investigated. Under the assumption that the input signal is a stationary Markov chain with rare transitions, it is shown that the information rate is asymptotically equivalent to the entropy of the chain and, therefore, the main term of its asymptotics does not depend on the channel noise.