On the Information Stability of Channels With Timing Errors

In this paper, we consider the class of channels corrupted by timing errors and intersymbol interference (ISI). The timing error is modeled as a discrete-time, discrete-valued random walk process. We prove that this class of channels are information stable for Markov input process of any finite order, and thereby, show achievable transmission rates in terms of asymptotic information rate. The proof we provide is extended from the proof by Dobrushin for the class of memoryless channels with independent timing errors