Entropy Density and Mismatch in High-Rate Scalar Quantization with Rényi Entropy Constraint
- 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 $\alpha$
| Author: | Wolfgang Kreitmeier, Tamas Linder |
|---|---|
| URN: | urn:nbn:de:bvb:739-opus-26132 |
| Document Type: | Preprint |
| Language: | German |
| Year of Completion: | 2011 |
| Date of Publication (online): | 2012/03/27 |
| Publishing Institution: | Universität Passau |
| Contributing Corporation: | Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada |
| Release Date: | 2012/03/27 |
| Tag: | Asymptotic quantization theory; Rényi-entropy; distortion density; entropy density; quantizer mismatch |
| GND Keyword: | Maßtheorie; Quantisierung; Entropie |
| Note: | 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 |
| Source: | IEEE Transactions on Information Theory Journal, ISSN: 0018-9448 |
| Institutes: | Fakultät für Informatik und Mathematik / Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| open_access (DINI-Set): | open_access |
| Licence (German): | Standardbedingung laut Einverständniserklärung |

