On Globally Optimal Encoding, Decoding, and Memory Update for Noisy Real-Time Communication Systems

The design of optimal joint source-channel communication strategies for a real-time com- munication system, i.e., a sequential communication system in which information must be transmitted and decoded withing axed-�nite delay, is considered. First, a system which runs for anite horizon and consists of arst-order Markov source, a real-time encoder, a memoryless noisy channel, a real-time decoder withnite memory, and distortion met- ric that accepts zero delay, is considered. The design of optimal real-time communication strategies is formulated as a decentralized stochastic optimization problem. There is no ex- isting solution methodology to solve general decentralized stochastic optimization problems overnite and innite horizon. This paper develops a systematic methodology, based on the notions of information structure and information state, to sequentially obtain globally optimal real-time encoding, decoding, and memory update strategies. Such a sequential decomposition results in a set of nested optimality equations whose solution determines an optimal communication strategy. This methodology is extended to two classes of innite- horizon systems, where optimal communication strategies are determined by the solution of an appropriate functional equation. The methodology is also extended to systems where distortion metric accepts axed-�nite delay, to systems with higher-order Markov sources, and to systems with channels with memory. Thus, this paper develops a comprehensive method to study dierent variations of real-time communication.