NDLI: A note on the existence of optimal entropy-constrained vector quantizers

Content Provider	IEEE Xplore Digital Library
Author	Gyorgy, A. Linder, T.
Copyright Year	2002
Description	Author affiliation: Dept. of Comput. Sci. & Inf. Theor., Budapest Univ. of Technol., Hungary (Gyorgy, A.)
Abstract	Chou and Betts (1998) showed that for any source distribution with sufficiently light tails the optimal entropy-constrained vector quantizer (ECVQ) has a finite number of code points. This result addressed those optimal vector quantizers that achieve the lower convex hull of the operational distortion-rate function, i.e., quantizers Q that minimize the Lagrangian performance D(Q)+/spl lambda/H(Q) for some /spl lambda/>0, where D(Q) is the quantizer's expected distortion and H(Q) is its output entropy. This Lagrangian optimality criterion also matches the Lloyd-type algorithm used to optimize ECVQs, and corresponds to the fixed-slope approach in variable-rate lossy source coding. The existence of Lagrangian-optimal quantizers, however, was an open question. In this paper we show that optimal ECVQs minimizing the Lagrangian performance always exist under general conditions on the source and the distortion measure. A related result showing the existence of a mean-square optimal ECVQ in the class of regular ECVQs is also presented.
Sponsorship	IEEE Inf. Theory Soc
File Size	136853
File Format	PDF
ISBN	0780375017
DOI	10.1109/ISIT.2002.1023309
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-06-30
Publisher Place	Switzerland
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lagrangian functions Distortion measurement Entropy Q measurement Computer science Information theory Probability distribution Source coding Random variables Quantization
Content Type	Text
Resource Type	Article

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