@unpublished{KreitmeierLinder2011, author = {Kreitmeier, Wolfgang and Linder, Tamas}, title = {Entropy Density and Mismatch in High-Rate Scalar Quantization with R{\´e}nyi Entropy Constraint}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus-26132}, year = {2011}, abstract = {Properties of scalar quantization with \$r\$th power distortion and constrained R\'enyi entropy of order \$\alpha\in (0,1)\$ are investigated. For an asymptotically (high-rate) optimal sequence of quantizers, the contribution to the R\'enyi entropy due to source values in a fixed interval is identified in terms of the "entropy density" of the quantizer sequence. This extends results related to the well-known point density concept in optimal fixed-rate quantization. A dual of the entropy density result quantifies the distortion contribution of a given interval to the overall distortion. The distortion loss resulting from a mismatch of source densities in the design of an asymptotically optimal sequence of quantizers is also determined. This extends Bucklew's fixed-rate (\$\alpha=0\$) and Gray \emph{et al.}'s variable-rate (\$\alpha=1\$)mismatch results to general values of the entropy order parameter \$\alpha\$}, subject = {Maßtheorie}, language = {de} } @unpublished{Kreitmeier2012, author = {Kreitmeier, Wolfgang}, title = {Asymptotic optimality of scalar Gersho quantizers}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus-27080}, year = {2012}, abstract = {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.}, subject = {Maßtheorie}, language = {en} }