Implicit communication in multiple-access settings

Optimal control strategies for decentralized control problems may involve internal communication between controllers. We think of such internal communication as implicit, since the messages being sent are endogenous to the system and not externally specified. Recently, Grover and Sahai [1] applied information-theoretic techniques to provide an approximately optimal scheme for the Witsenhausen counterexample: one of the simplest models of a decentralized control system. This paper examines a MAC-inspired extension of the Witsenhausen counterexample. Deterministic modeling techniques based on the work by Avestimehr at al. [2] feature centrally in the strategy development. This example illustrates that “Information is in the eye of the beholder”, and we find “rate gains” in the context of implicit communication. These are not observed in the original Witsenhausen counterexample.