Channels with Action Dependent States and Additional Private Messages

In channels with action dependent states, a message is conveyed using two encoders operating sequentially, viz.an action encoder and a channel encoder. The actions drive the output of a discrete-memoryless channel (DMC),which in turn forms the state process for the DMC between the channel encoder and receiver. Assuming non-causalknowledge of the state-process at the channel encoder, a single letter characterization of the capacity is known inthe discrete memoryless case.We consider the action dependent state channel where an additional private message needs to be communicatedby the channel encoder. In addition, we consider a common reconstruction (CR) of the state at the channel encoderand decoder. Capacity characterizations for the discrete memoryless and Gaussian versions are presented. As aconsequence, we settle the capacity characterization of the Gaussian action dependent channel with only a commonmessage and CR. We further show that the availability of strictly causal state feedback to the action encoder, evenwith randomization allowed, does not improve the capacity of the action dependent state channel.