Witsenhausen’s counterexample as Assisted Interference Suppression

Despite the seemingly irreducible simplicity of Witsenhausen’s counterexample, the optimal control law for the problem is not yet known. It has been observed that the counterexample contains an implicit communication problem. We formulate a vector version of the Witsenhausen counterexample that helps simplify the problem further while preserving its essential character. The vector version of the counterexample is shown to correspond to a previously unstudied communication problem which we dub “Assisted Interference Suppression.” Using concepts of lossy compression, channel coding, and dirtypaper coding, nonlinear control strategies are developed that outperform the optimal linear laws in the limit of large vector lengths for this new problem. The proposed techniques also outperform the best affine strategy and the known scalar strategies by an unbounded factor. A new lower bound is also developed using information-theoretic arguments that is sometimes better than that derived by Witsenhausen.