Adaptive vector quantization-Part I: a unifying structure

Abstract

Summary form only given. Although rate-distortion theory establishes optimal coding properties for vector quantization (VQ) of stationary sources, the fact that real sources are, in actuality, nonstationary has led to the proposal of adaptive-VQ (AVQ) algorithms that compensate for changing source statistics. Because of the scarcity of rate-distortion results for nonstationary sources, proposed AVQ algorithms have been mostly heuristically, rather than analytically, motivated. As a result, there has been, to date, little attempt to develop a general model of AVQ or to compare the performance associated with existing AVQ algorithms. We summarize observations resulting from detailed studies of a number of previously published AVQ algorithms. To our knowledge, the observations represent the first attempt to define and describe AVQ in a general framework. We begin by proposing a mathematical definition of AVQ. Because of the large variety of algorithms that have purported to be AVQ, it is unclear from prior literature precisely what is meant by this term. Any resulting confusion is likely due to a certain imprecise, and sometimes ambiguous, use of the word "adaptive" in VQ literature. However, common to a large part of this literature is the notion that AVQ properly refers to techniques that dynamically vary the contents of a VQ codebook as coding progresses. Our definition of AVQ captures this idea of progressive codebook updating in a general mathematical framework.