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We study the problem of zero-delay coding of a Markov source over a noisychannel with feedback. We first formulate the problem as a Markov decisionprocess (MDP) where the state is a previous belief term along with a finitememory of channel outputs and quantizers. We then approximate this state bymarginalizing over all possible beliefs, so that our policies only use thefinite-memory term to encode the source. Under an appropriate notion ofpredictor stability, we show that such policies are near-optimal for thezero-delay coding problem as the memory length increases. We also givesufficient conditions for predictor stability to hold, and propose areinforcement learning algorithm to compute near-optimal finite-memorypolicies. These theoretical results are supported by simulations.

Near-Optimality of Finite-Memory Codes and Reinforcement Learning for Zero-Delay Coding of Markov Sources