On the Capacity of Channels with Markov Insertions, Deletions and Substitutions

We consider channels with synchronization errors. A classical result for such channels is their information stability, when the synchronization errors are memoryless. In this paper, we extend this result to the case where the synchronization errors have memory. Specifically, we assume that the synchronization errors are governed by a stationary and ergodic finite state Markov chain, and prove that such channel is information-stable, which implies the existence and achievability of the limit of normalized mutual information. This result applies to a wide range of channels with synchronization errors, with different applications including DNA storage. The developed methodology may also be useful to prove other coding theorems for non-trivial channel sequences.