An achievability proof for the lossy coding of Markov sources with feed-forward

The lossy source coding problem with feed-forward link was recently introduced in [1] and the corresponding rate-distortion function was derived in [2] and [3] for stationary and ergodic sources and for arbitrary sources with memory, respectively. The achievability schemes of [2] and [3] are mainly based on codetrees. In this work, we give an alternative proof of achievability for binary asymmetric Markov sources via a simple coding scheme that utilizes optimal lossy coding for Bernoulli sources. We then generalize this coding scheme for m-ary Markov sources and show its optimality for the distortion region where the Shannon lower bound is tight.