Message and State Communication over Channels with Action Dependent States

In an action dependent state channel (ADSC), there are two encoders, viz. an action encoder and a channel encoder. We consider a Gaussian ADSC (GADSC) setup where the state process is generated by passing the action symbols through an AWGN channel. The receiver observes the superposition of the channel encoder symbols, state process, and independent AWGN.In our model, in addition to decoding the messages, the receiver is required to produce an estimate of the state process within some prescribed mean-squared error distortion. While joint state estimation and communication for a discrete memoryless ADSC with strictly causal state information has been solved, its non-causal counterpart remains open. We resolve this for the GADSC under average power constraints at the two encoders. Furthermore, we allow an additional independent message stream at the channel encoder and characterize the optimal distortion-rate trade-off region. Interestingly, our results also characterize the capacity region of a state-dependent Gaussian multiple access channel (MAC) with degraded message sets and state estimation constraints.