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On optimal causal coding of partially observed Markov sources under classical and non-classical information structures

The optimal real-time coding of a partially observed Markov process is studied, where the cost to be minimized is an arbitrary non-negative, additive, single-letter function of the source and the decoder output. Both centralized and decentralized settings are considered. A structural result is obtained extending Witsenhausen's structural results on the optimal realtime coders to a partially observed setting. The decentralized-control concept of signaling (the action that decision makers communicate via their actions) is interpreted in a real-time decentralized coding setting. When signaling is present, a counterexample to a natural separation conjecture is presented.