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Title: Asymptotic analysis of digital transmission systems for a first order Gauss-Markov process 
Author: Shankar, H (Hari)
Date: 1991
Abstract: In this dissertation, we examine the problem of transmitting a first order Gauss-Markov process over a noiseless digital channel for large transmission rates. We address the problem of minimizing the time averaged mean square error, for a fixed transmission rate of r bits per second, by finding the optimum sampling rate and the optimum number of quantization levels. The performance of different reconstruction filters is first examined. Optimal nonlinear reconstruction filters are approximated by linear filters. Fine quantization techniques are used to analyze the performance of different quantization schemes. Fine quantization techniques have been traditionally used to evaluate the variance of the quantization error. These techniques have been extended to evaluate expectations of other functions of the quantization error. The results are used to study the performance of mismatched quantizers, i.e. quantizers that are not optimized exactly for their source statistics. The optimum quantization of two different random variables is also studied; approximations for the correlation between the input of one quantizer and the quantization error of the other and for the correlation between their quantization errors are found. These results form a powerful set of tools with which more complex quantization systems can be analyzed. We study the minimum time averaged error that can be achieved by different quantization systems for a fixed transmission rate and also compare the power spectral densities of their quantization error. PCM, matched and mismatched DPCM and Sigma-Delta modulation are analyzed. The improvement in performance that can be obtained by adding memory to a quantizer is examined. To this end, a modified PCM scheme that contains sufficient memory in the receiver to store the previous output of the transmitter is examined. We also describe a finite state sliding block quantizer and study its performance as a function of the memory in the transmitter and the receiver.
Description: Thesis (Ph. D.)--University of Hawaii at Manoa, 1991. Includes bibliographical references (leaves 124-125) Microfiche. ix, 125 leaves, bound ill. 29 cm
Rights: All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.

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