Finding the best mismatched detector for channel coding and hypothesis testing

The mismatched-channel formulation is generalized to obtain simplified algorithms for computation of capacity bounds and improved signal constellation designs. The following issues are addressed: (i) For a given finite dimensional family of linear detectors, how can we compute the best in this class to maximize the reliably received rate? That is, what is the best mismatched detector in a given class? (ii) For computation of the best detector, a new algorithm is proposed based on a stochastic approximation implementation of the Newton-Raphson method, (iii) The geometric setting provides a unified treatment of channel coding and robust/adaptive hypothesis testing.