We consider channels with synchronization errors modeled as insertions and deletions. A classical result for such channels is their information stability, 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 such channel is information-stable, which implies the existence of a coding scheme which achieves the limit of mutual information. This result implies the existence of the Shannon capacity for a wide range of channels with synchronization errors, with different applications including DNA storage. The methods developed may also be useful to prove other coding theorems for non-trivial channel sequences.

翻译：我们考虑同步错误建模为插入和删除的信道。这类信道的一个经典结果是其信息稳定性，从而在同步错误无记忆时存在香农容量。在本文中，我们将这一结果推广到插入和删除具有记忆性的情形。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，并证明此类信道是信息稳定的，这意味着存在一种能实现互信息极限的编码方案。该结果证明，对于包括DNA存储在内的多种具有同步错误的应用场景，香农容量均存在。文中发展的方法也可能有助于证明其他非平凡信道序列的编码定理。