3 . 3 Improved ratio using Dirty - Paper Coding ( DPC ) based strategies

(x1 − x̂1) 2 ] The Witsenhausen counterexample [Witsenhausen’68] is a distributed Linear-Quadratic-Gaussian problem for which nonlinear control laws outperform the optimal linear control law. The optimal control law is still elusive — and the non-Gaussian relaxation of the problem is known to be NPcomplete [Papadimitriou and Tsitsiklis ’86]. The counterexample has an implicit channel that makes it hard. The first controller modifies the initial state and attempts to communicate themodified state to the second controller through a noisy channel. Solving the problem of minimizing MMSE error in estimating x̂1 with an average power constrained u1 is an equivalent formulation.