Scalar Quantization II:Optimality and Design

Abstract

In the previous chapter, we focused on the characterization of quantizers and the assessment of the performance of a given quantizer. The second and more important issue from the engineer’s perspective is the design and implementation of quantizers to meet performance objectives. As always in engineering, there are conflicting objectives and compromise is needed. To provide the tools to find the best trade-off, it is first necessary to understand what is the best that can be achieved under the given constraints. We first focus on the question of quantizer optimality. Specifically, given the constraint that the number of levels, N,is fixed, we examine the conditions that the optimal quantizer must satisfy in order to minimize the average distortion for a particular input pdf. Having established the two key necessary conditions for optimality, we then examine how they can be used to obtain design algorithms of practical use for particular situations. We then go on to discuss implementation issues.