Improved performance bounds for the infinite-dimensional Witsenhausen problem

There is a growing concern regarding the design of decentralized control systems. Witsenhausen's counterexample is a well-known problem which has remained open in this context, and emphasizes the necessity of communication between blocks in a distributed control system. In this paper, we study an infinite vector model of this problem and a new bound for the cost function is derived. It is shown that this bound improves upon previously known bounds obtained by dirty paper coding in some SNR regimes. Consequently, a system can be designed to sense the SNR level and then select the best scheme between these two sub-optimal strategies.