On Optimal Causal Coding of Partially Observed Markov Sources in Single and Multi-Terminal Settings

The optimal causal coding of a partially observed Markov process is studied, where the cost to be minimized is a bounded, non-negative, additive, measurable single-letter function of the source and the receiver output. A structural result is obtained extending Witsenhausen's and Walrand-Varaiya's structural results on optimal real-time coders to a partially observed setting. The decentralized (multi-terminal) setup is also considered. For the case where the source is an i.i.d. process, it is shown that the optimal decentralized causal coding of correlated observations problem admits a solution which is memoryless. For Markov sources, a counterexample to a natural separation conjecture is presented.