Action dependent strictly causal state communication

Channels with action-dependent states are considered: given the message to be communicated, the transmitter chooses an action sequence that affects the formation of the channel states, and then creates the channel input sequence based on the observed state sequence. The capacity - distortion tradeoff of such a channel is characterized for the case when the state information is available strictly causally at the channel encoder. The problem setting extends the action dependent framework of [1] and as a special case recovers the results of few previously considered joint communication and estimation scenarios in [2], [3], [4]. The scenario when the action is also allowed to depend on the past observed states is also considered and it has been shown that such adaptive action helps in achiveing a better capacity - distortion function.