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The optimal causal (zero-delay) coding of a partially observed Markov process is studied, where the cost to be minimized is a bounded, nonnegative, 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 causal coders to more general state spaces and to a partially observed setting. The decentralized (multiterminal) setup is also considered. For the case where the source is an i.i.d. process, it is shown that an optimal solution to the decentralized causal coding of correlated observations problem is memoryless. For Markov sources, a counterexample to a natural separation conjecture is presented.

On Optimal Causal Coding of Partially Observed Markov Sources in Single and Multiterminal Settings