  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.
