Solutions to a class of linear-quadratic-Gaussian (LQG) stochastic team problems with nonclassical information

We consider a stochastic dynamic team problem with two controllers and nonclassical information, which can be viewed as the transmission of a garbled version of a Gaussian message over a number of noisy channels under a fidelity criterion. We show that the optimum solution (under a quadratic loss functional) consists of linearly transforming the garbled message to a certain (optimum) power level P^* and then optimally decoding it by using a linear transformation at the receiving end. The power level P^* is determined by the solution of a fifth order algebraic equation. The paper also discusses an extension of this result to the case when the channel noise is correlated with the input random variable, and shows that for the single channel case the optimum solution is again linear.