Asymptotic optimality of scalar Gersho quantizers

  • In his famous paper Gersho stressed that the codecells of optimal quantizers asymptotically make an equal contribution to the distortion of the quantizer. Motivated by this fact, we investigate in this paper quantizers in the scalar case, where each codecell contributes with exactly the same portion to the quantization error. We show that such quantizers of Gersho type - or Gersho quantizers for short - exist for non-atomic scalar distributions. As a main result we prove that Gersho quantizers are asymptotically optimal.

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Metadaten
Author:Wolfgang Kreitmeier
URN:urn:nbn:de:bvb:739-opus-27080
Document Type:Preprint
Language:English
Year of Completion:2012
Date of Publication (online):2013/10/09
Publishing Institution:Universität Passau
Release Date:2013/10/09
Tag:Quantisierung
Asymptotically optimal quantization; Gersho quantizer; High rate quantization; Quantization error; Scalar quantization
GND Keyword:Maßtheorie; Informationstheorie; Signaltheorie; Approximation; Kodierung
Note:
This is a preprint of an article accepted for publication in Constructive Approximation, ISSN: 0176-4276 (print version) ISSN: 1432-0940 (electronic version) Copyright (c) by Springer. The final publication is available at link.springer.com URL: http://dx.doi.org/10.1007/s00365-013-9214-2
Source:Constructive Approximation ISSN: 0176-4276 (print version) ISSN: 1432-0940 (electronic version)
Institutes:Fakultät für Informatik und Mathematik / Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A29 Approximation with constraints
open_access (DINI-Set):open_access
Licence (German):License LogoStandardbedingung laut Einverständniserklärung