Channels with Action Dependent States and Common Reconstructions

In channels with action dependent states, a common 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-causal knowledge of the state-process at the channel encoder, a single letter characterization of the capacity is known in the discrete memoryless case. We consider the action dependent state channel with a common message and an additional private message at the channel encoder, along with common reconstructions (CR) of the state process at the channel encoder and the decoder. Capacity characterizations for the discrete memoryless and Gaussian versions are presented. As a consequence, we settle the capacity characterization of the Gaussian action dependent channel with only a common message and CR. Moreover, by identifying a connection to degraded message sets multiple access channel (deg-MAC) models studied in literature, we establish the capacity regions for the discrete and Gaussian versions of deg-MAC with CR constraints.