Optimal real-time encoder-decoding of Markov sources over noisy channels

A real-time communication system consisting of a first-order Markov source, a real-time encoder, a discrete memoryless channel, and a real-time decoder is considered. The quality of reconstruction is determined by a distortion function between the current source output and its reconstruction at the decoder. The distortion function does not accept delays. The objective is to choose encoding and decoding strategies to minimize the total expected distortion over a finite horizon. The problem is modelled as a decentralized stochastic control problem. A two step solution methodology is developed which provides a sequential decomposition of the problem and reduces exponentially the complexity to search for an optimal solution. The key step of our methodology is identifying information state sufficient for performance evaluation. The methodology can be extended to real-time communication problems with noisy feedback, feedback control problems with a noisy channel in the feedback loop, and decentralized diagnosis in logical discrete event systems.