Vector quantization in speech coding

TLDR

Quantization converts continuous signals into discrete digital values for data compression, with scalar quantization treating each value independently and vector quantization jointly exploiting linear and nonlinear dependencies, probability density shape, and dimensionality to remove redundancy. This tutorial review aims to present the fundamental concepts of vector quantization and evaluate its benefits and costs relative to scalar quantization. The review illustrates these concepts with simple examples, discusses theoretical performance limits from rate‑distortion theory, and examines practical design, implementation, and application issues, focusing mainly on speech signal coding. The authors demonstrate that vector quantization achieves performance gains by exploiting multidimensional dependencies, as shown by the theoretical limits reviewed and the example illustrations.

Abstract

Quantization, the process of approximating continuous-amplitude signals by digital (discrete-amplitude) signals, is an important aspect of data compression or coding, the field concerned with the reduction of the number of bits necessary to transmit or store analog data, subject to a distortion or fidelity criterion. The independent quantization of each signal value or parameter is termed scalar quantization, while the joint quantization of a block of parameters is termed block or vector quantization. This tutorial review presents the basic concepts employed in vector quantization and gives a realistic assessment of its benefits and costs when compared to scalar quantization. Vector quantization is presented as a process of redundancy removal that makes effective use of four interrelated properties of vector parameters: linear dependency (correlation), nonlinear dependency, shape of the probability density function (pdf), and vector dimensionality itself. In contrast, scalar quantization can utilize effectively only linear dependency and pdf shape. The basic concepts are illustrated by means of simple examples and the theoretical limits of vector quantizer performance are reviewed, based on results from rate-distortion theory. Practical issues relating to quantizer design, implementation, and performance in actual applications are explored. While many of the methods presented are quite general and can be used for the coding of arbitrary signals, this paper focuses primarily on the coding of speech signals and parameters.