  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.
