arXiv subjects

Wolfgang Kreitmeier

Publications and source records attributed to Wolfgang Kreitmeier.

4 recordsLinked to original sources

arXiv2013

Asymptotic optimality of scalar Gersho quantizers

In his famous paper [7] Gersho stressed that the codecells of optimal quantizers asymptotically make an equal contribution to the distortion of the quantizer. Motivated by this fact, we investigate in this paper quantizers in the scalar case, where each codecell contributes with exactly the same portion to the quantization error. We will show that such quantizers of Gersho type - or Gersho quantizers for short - exist for non-atomic scalar distributions. As a main result we will prove that Gersho quantizers are asymptotically optimal.

math.FA↗

arXiv2013

Quantization of Gaussian measures with Rényi-α-entropy constraints

We consider the optimal quantization problem with Rényi-$α$-entropy constraints for centered Gaussian measures on a separable Banach space. For $α= \infty$ we can compute the optimal quantization error by a moment on a ball. For $α\in {}]1,\infty]$ and large entropy bound we derive sharp asymptotics for the optimal quantization error in terms of the small ball probability of the Gaussian measure. We apply our results to several classes of Gaussian measures. The asymptotical order of the optimal quantization error for $α> 1$ is different from the well-known cases $α= 0$ and $α= 1$.

math.PR↗

arXiv2012

Entropy Density and Mismatch in High-Rate Scalar Quantization with Renyi Entropy Constraint

Properties of scalar quantization with $r$th power distortion and constrained Rényi entropy of order $α\in (0,1)$ are investigated. For an asymptotically (high-rate) optimal sequence of quantizers, the contribution to the Rényi 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 ($α=0$) and Gray \emph{et al.}'s variable-rate ($α=1$) mismatch results to general values of the entropy order parameter $α$.

cs.IT↗

arXiv2011

High-resolution scalar quantization with Rényi entropy constraint

We consider optimal scalar quantization with $r$th power distortion and constrained Rényi entropy of order $α$. For sources with an absolutely continuous distribution the high rate asymptotics of the quantizer distortion has long been known for $α=0$ (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 $α\in [-\infty,0)\cup (0,1)$. The achievability proof is based on finding (asymptotically) optimal quantizers via the companding approach, and is thus constructive.

cs.IT↗