
Accession Number : AD0669097
Title : AN INVESTIGATION OF QUANTIZATION TECHNIQUES.
Descriptive Note : Final rept. 29 Nov 6628 Feb 68,
Corporate Author : SIGNATRON INC LEXINGTON MASS
Personal Author(s) : Gish,Herbert
Report Date : FEB 1968
Pagination or Media Count : 53
Abstract : The report consists of two parts, each developing a different approach to the efficient quantization of analog sources. In Part I, it is shown, under weak assumptions on the density function of a random variable, and under weak assumptions on the error criterion, that uniform quantizing yields an output entropy which asymptotically is smaller than that for any other quantizer, independent of the density function or the error criterion. The asymptotic behavior of the rate distortion function is determined for the class of nuth law loss functions and the entropy of the uniform quantizer is compared with the rate distortion function for this class of loss functions. The extension of these results to the quantizing of sequences is also given. It is shown that the discrepancy between the entropy of the uniform quantizer and the rate distortion function apparently lies with the inability of the optimal quantizing shapes to cover large dimensional spaces without overlap. A comparison of the entropies of the uniform quantizer and of the minimumalphabet quantizer is also given. In Part II, predictive quantization systems and their optimality properties are discussed. A technique for the estimation of the performance of such systems is presented which is then compared to the results of a digital simulation. (Author)
Descriptors : (*INFORMATION THEORY, OPTIMIZATION), CODING, RANDOM VARIABLES, STATISTICAL ANALYSIS, ERRORS, DIGITAL SYSTEMS, ANALOG SYSTEMS, SEQUENCES(MATHEMATICS), PERFORMANCE(ENGINEERING), MATHEMATICAL PREDICTION, SIMULATION
Subject Categories : Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE