High-Resolution Scalar Quantization with Rényi Entropy Constraint
- We consider optimal scalar quantization with $r$th power distortion and constrained R\'enyi entropy of order $\alpha$. For sources with absolutely continuous distributions the high rate asymptotics of the quantizer distortion has long been known for $\alpha=0$ (fixed-rate quantization) and $\alpha=1$ (entropy-constrained quantization). These results have recently been extended to quantization with R\'enyi entropy constraint of order $\alpha \ge r+1$. Here we consider the more challenging case $\alpha\in [-\infty,0)\cup (0,1)$ and for a large class of absolutely continuous source distributions we determine the sharp asymptotics of the optimal quantization distortion. The achievability proof is based on finding (asymptotically) optimal quantizers via the companding approach, and is thus constructive.
| Author: | Wolfgang Kreitmeier, Tamas Linder |
|---|---|
| URN: | urn:nbn:de:bvb:739-opus-23787 |
| Document Type: | Preprint |
| Language: | German |
| Year of Completion: | 2011 |
| Date of Publication (online): | 2011/07/08 |
| Publishing Institution: | Universität Passau |
| Release Date: | 2011/07/08 |
| Tag: | Companding; Rényi entropy; high-resolution asymptotics; optimal quantization |
| 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 |

