On the capacity of the one-bit deletion and duplication channel

The one-bit deletion and duplication channel is investigated. An input to this channel consists of a block of l ≥ 1 bits which experiences a deletion with probability p, a duplication with probability q, and remains unchanged with probability 1 - p - q. For this channel a capacity expression is obtained in the asymptotic regime where p + q = o(l/logl). As a corollary, we obtain an asymptotic expression for the capacity of the so called "segmented" deletion and duplication channel where the input now consists of several blocks and each block independently experiences either a deletion, or a duplication, or remains unchanged.