TY - INPR A1 - Kreitmeier, Wolfgang T1 - Asymptotic optimality of scalar Gersho quantizers N2 - 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. KW - Maßtheorie KW - Informationstheorie KW - Signaltheorie KW - Approximation KW - Kodierung KW - Quantisierung KW - Asymptotically optimal quantization KW - Quantization error KW - Scalar quantization KW - Gersho quantizer KW - High rate quantization Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus-27080 N1 - 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 ER -