Optimality of Walrand-Varaiya type policies and approximation results for zero delay coding of Markov sources

Optimal zero-delay coding (quantization) of a finite-state Markov source is considered. Building on our earlier work and previous literature, using a stochastic control problem formulation, the existence and structure of optimal quantization policies are studied. Our main result establishes, for infinite horizon problems, the optimality of deterministic and stationary (Walrand-Varaiya type) Markov coding policies. In addition, the ε-optimality of finite-memory quantizers is established and the dependence between the memory length and ε is quantified. Numerical results are also presented.