Applications of Ali-Silvey Distance Measures in the Design Generalized Quantizers for Binary Decision Systems

The Ali-Silvey class of distance measures is applied to the problem of designing quantizers for use in binary detection systems. To find optimal solutions the notion of quantization must be generalized slightly, and necessary conditions are established for the selection of quantizer parameters in this context. Local, or small-signal, conditions are also derived and these are seen to agree with asymptotic results based on Pitman efficiency. As an example, four-level generalized quantization for detecting a constant signal in additive generalizedGaussian noise is investigated.