Bounds on mutual information rates of noisy channels with timing errors

In this paper, we consider the information rates of baseband linear filter channels with timing errors. We assume that the timing error can be modeled as a discrete-valued Markov process. Based on this assumption, we turn the channel into a finite-state machine model and show that the output sequence is an ergodic and asymptotically stationary hidden Markov process. We then propose Monte-Carlo methods to compute the upper and lower bounds on the information rate by utilizing the entropy ergodic theorem