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.

翻译：我们考虑以插入和删除为模型的同步错误信道。此类信道的一个经典结果是，当同步错误是无记忆时，信道具有信息稳定性，从而存在香农容量。在本文中，我们将此结果推广到插入和删除具有记忆性的情况。具体而言，我们假设同步错误由平稳且遍历的有限状态马尔可夫链控制，并证明此类信道的互信息容量存在，且等于其编码容量，这表明存在一种能够达到该极限的编码方案。