Input-constrained erasure channels: Mutual information and capacity

In this paper, we derive an explicit formula for the entropy rate of a hidden Markov chain, observed when the Markov chain passes through a memoryless erasure channel. This result naturally leads to an explicit formula for the mutual information rate of memoryless erasure channels with Markovian inputs. Moreover, if the input Markov chain is of first-order and supported on the (1, ∞)-run length limited (RLL) constraint, we show that the mutual information rate is strictly concave with respect to a chosen parameter. Then we apply a recent algorithm [1] to approximately compute the first-order noisy constrained channel capacity and the corresponding capacity-achieving distribution.