MULTIDIMENSIONAL QUANTIZER DESIGN

KERRY DAVID RINES, Purdue University

Abstract

Multidimensional quantization for the encoding of analog sources has received increasing attention in recent years. The theoretical advantages of multidimensional quantizers over one-dimensional quantizers have been studied in the literature. The results indicate that the potential exists to improve digital encoders by replacing one-dimensional quantizers with quantizers of a higher dimension. Unfortunately the design and implementation of multidimensional quantizers has proved to be very difficult. Recently, computer algorithms that specify the optimum set of output vectors for multidimensional quantizers have been developed. These optimum quantizers are implemented using a search procedure to choose, from the specified output set, the output vector that is the smallest distance from the input. One disadvantage of the search procedure is that the storage and computation time requirements increase with the number of output vectors and the dimension of the quantizer. As a result it may be impossible to implement the optimum quantizer when the dimension or the number of quantization levels is very large. In this thesis we develop two new approaches for the design of multidimensional quantizers. First we present a technique called prequantization. With prequantization we can design optimum uniform multidimensional quantizers using one-dimensional quantizers and zero-memory nonlinearities. These quantizers are easy to implement and compute the output vectors directly without the use of a search. For the design of nonuniform quantizers, a piecewise companding approach is developed. While not optimum, piecewise companding can be used to design near-optimum quantizers for random vectors having any multidimensional density function. As with prequantization the piecewise companding designs represent a substantial improvement over the quantizer designs based on a search.

Degree

Ph.D.

Subject Area

Electrical engineering

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