On the Capacity of Channels with Deletions and States

Abstract: We consider the class of channels formed from the concatenation of a deletion channel and a finite-state channel. For this class of channels, we show that the operational capacity is equal to the stationary capacity, which can be approached by a sequence of Markov processes with increasing Markovian orders. As a by-product, we show that the polar coding scheme constructed by Tal, Pfister, Fazeli and Vardy achieves the capacity of the deletion channel.