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Optimal quantization for dyadic homogeneous Cantor distributions
Author(s) -
Kreitmeier Wolfgang
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510680
Subject(s) - mathematics , homogeneous , quantization (signal processing) , dimension (graph theory) , class (philosophy) , pure mathematics , mathematical analysis , combinatorics , statistics , artificial intelligence , computer science
For a large class of dyadic homogeneous Cantor distributions in ℝ, which are not necessarily self‐similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non‐existence of the quantization coefficient. The class contains all self‐similar dyadic Cantor distributions, with contraction factor less than or equal to 1/3. For these distributions we calculate the quantization errors explicitly. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)