Generalized vector quantization: jointly optimal quantization and estimation

The important conditions and properties of the optimal generalized vector quantizer are presented. However, the optimal encoder has, in general, unmanageable complexity since its partition regions may neither convex nor connected. Hence, it is proposed to constrain the complexity of the encoder by restricting its structure. Finding the optimal GVQ subject to the structural constraint is hard optimization problem and to address it, ideas from statistical physics has to be applied. Although this approach is extendible to a variety of structures, the derivation is limited to the specific structure of the multiple prototype classifier called the multiple-prototype generalized vector quantizer (MP-GVQ). The usefulness of MP-GVQ design procedure for a variety of source coding is demonstrated.