Shannon Capacity of Channels with Markov Insertions, Deletions and Substitutions

We consider channels with synchronization errors modeled as insertions and deletions. A classical result for such channels is the information stability of such channels, hence the existence of the Shannon capacity, when the synchronization errors are memoryless. In this paper, we extend this result to the case where the insertions and deletions have memory. Specifically, we assume that the synchronization errors are governed by a stationary and ergodic finite state Markov chain, and prove that mutual information capacity of such channels exist, and it is equal to its coding capacity, showing that there exists a coding scheme which achieves this limit.