Optimality of Stationary and Deterministic Policies for Zero-Delay Coding of ℝd-Valued Linear Markov Sources with Quadratic Cost

Optimal zero-delay coding (fixed-rate quantization) of ℝ
^d
-valued linear Markov sources is studied. The structure and existence of deterministic and stationary coding policies for the infinite horizon average cost problem is established. Prior results in the literature studying optimality results for Markov sources under infinite horizons either considered finite alphabet sources or, for ℝ
^d
-valued case, only established the existence of deterministic and non-stationary Markov coding policies or those which are randomized. In addition to existence results, the finite blocklength (time horizon) performance of an optimal (stationary and Markov) coding policy is shown to approach the infinite time horizon optimum at a rate O(1/T ).