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

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

2011-08-08

arxiv.org/abs/1108.1730v2

Computer Science

Information Theory

25 pages

Scientific paper

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 $\alpha$.

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