Optimal Zero Delay Coding of Markov Sources: Stationary and Finite Memory Codes

作     者：Wood, Richard G. Linder, Tamas Yuksel, Serdar 

作者机构：Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada 

出 版 物：《IEEE TRANSACTIONS ON INFORMATION THEORY》 

年 卷 期：2017年第63卷第9期

页      面：5968-5980页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Natural Sciences and Engineering Research Council of Canada 

主　　题：Zero delay source coding real time coding causal coding quantization stochastic control Markov sources Markov decision processes 

摘      要：The optimal zero delay coding of a finite-state Markov source is considered. The existence and structure of optimal codes are studied using a stochastic control formulation. Prior results in the literature established the optimality of deterministic Markov (Walrand-Varaiya-type) coding policies for the finite time horizon problem, and the optimality of both deterministic nonstationary and randomized stationary policies for the infinite time horizon problem. Our main result here shows that for any irreducible and aperiodic Markov source with a finite alphabet, deterministic and stationary Markov coding policies are optimal for the infinite horizon problem. In addition, the finite block length (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). The results are extended to systems, where zero delay communication takes place across a noisy channel with noiseless feedback.