@unpublished{KreitmeierLinder2011, author = {Kreitmeier, Wolfgang and Linder, Tamas}, title = {Entropy Density and Mismatch in High-Rate Scalar Quantization with R{\´e}nyi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} }