Trellis quantization

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.