On globally optimal real-time encoding and decoding strategies in multi-terminal communication systems

We consider a communication system consisting of two encoders communicating with a single receiver over a noiseless channel. The two encoders make distinct partial observations of a discrete-time Markov source. Each encoder must encode its observations into a sequence of discrete variables. The sequence is transmitted over a noiseless channel to a receiver which attempts to reproduce the output of the Markov source. The system must operate in real-time, that is, the encoding at each encoder and decoding at the receiver must be performed without any delay. The goal is to find globally optimal real-time encoding and decoding strategies to minimize an expected distortion metric over a finite time horizon. We determine qualitative properties of optimal real-time encoding and decoding strategies. Using these properties, we develop a sequential decomposition of the problem of finding globally optimal real-time encoding and decoding strategies. Such a sequential decomposition reduces the complexity of the global optimization problem.