Channels with Action Dependent States and Additional Private Messages

Abstract

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-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 where an additional private message needs to be communicated by the channel encoder. In addition, we consider a common reconstruction (CR) of the state at the channel encoder and 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. We further show that the availability of strictly causal state feedback to the action encoder, even with randomization allowed, does not improve the capacity of the action dependent state channel.