TY - INPR A1 - Kreitmeier, Wolfgang A1 - Linder, Tamas T1 - High-Resolution Scalar Quantization with Rényi Entropy Constraint N2 - 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. KW - Maßtheorie KW - Quantisierung KW - Entropie KW - Companding KW - high-resolution asymptotics KW - optimal quantization KW - Rényi entropy Y1 - 2011 UR - https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/145 UR - https://nbn-resolving.org/urn:nbn:de:bvb:739-opus-23787 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 -