MAC with Action-Dependent State Information at One Encoder

Abstract: Problems dealing with the ability to take an action that affects the states of state-dependent communication channels are of timely interest and importance. Therefore, we extend the study of action-dependent channels, which until now focused on point-to-point models, to multiple-access channels (MAC). In this paper, we consider a two-user, state-dependent MAC, in which one of the encoders, called the informed encoder, is allowed to take an action that affects the formation of the channel states. Two independent messages are to be sent through the channel: a common message known to both encoders and a private message known only to the informed encoder. In addition, the informed encoder has access to the sequence of channel states in a non-causal manner. Our framework generalizes previously evaluated settings of state dependent point-to-point channels with actions and MACs with common messages. We derive a single letter characterization of the capacity region for this setting. Using this general result, we obtain and compute the capacity region for the Gaussian action-dependent MAC. The unique methods used in solving the Gaussian case are then applied to obtain the capacity of the Gaussian action-dependent point-to-point channel; a problem was left open until this work. Finally, we establish some dualities between action-dependent channel coding and source coding problems. Specifically, we obtain a duality between the considered MAC setting and the rate distortion model known as "Successive Refinement with Actions". This is done by developing a set of simple duality principles that enable us to successfully evaluate the outcome of one problem given the other.