TY - INPR A1 - Kreitmeier, Wolfgang A1 - Linder, Tamas T1 - Entropy Density and Mismatch in High-Rate Scalar Quantization with Rényi Entropy Constraint N2 - 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 $\alpha$ KW - Maßtheorie KW - Quantisierung KW - Entropie KW - Asymptotic quantization theory KW - distortion density KW - entropy density KW - quantizer mismatch KW - Rényi-entropy Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus-26132 N1 - This is a preprint of an article accepted for publication in the IEEE Transactions on Information Theory Journal, ISSN: 0018-9448. The original publication is available at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18 ER -