High-resolution scalar quantization with R\'enyi entropy constraint

Wolfgang Kreitmeier; Tamas Linder

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arXiv · 1008.1744

High-resolution scalar quantization with R\'enyi entropy constraint

Wolfgang Kreitmeier·Tamas Linder

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Abstract

We consider optimal scalar quantization with $r$th power distortion and constrained R\'enyi entropy of order $\alpha$. For sources with an absolutely continuous distribution the high rate asymptotics of the quantizer distortion has long been known for $\alpha=0$ (fixed-rate quantization) and $\al pha=1$ (entropy-constrained quantization). For a large class of absolutely continuous source distributions we determine the sharp asymptotics of the optimal quantization distortion for $\alpha\in [-\infty,0)\cup (0,1)$. The achievability proof is based on finding (asymptotically) optimal quantizers via the companding approach, and is thus constructive.

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Wolfgang Kreitmeier, Tamas Linder. 2010-08-10. High-resolution scalar quantization with R\'enyi entropy constraint. https://arxiv.org/abs/1008.1744

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