Information Rate in Memoryless Channels for a Slowly Varying Markov Signal

The problem of the calculation of information rate in stationary memoryless channels with an additive noise and a slowly varying input signal is considered. 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.