A Zador-Like Formula for Quantizers Based on Periodic Tilings
Abstract
We consider Zador's asymptotic formula for the distortion-rate function for a variable-rate vector quantizer in the high-rate case. This formula involves the differential entropy of the source, the rate of the quantizer in bits per sample, and a coefficient G which depends on the geometry of the quantizer but is independent of the source. We give an explicit formula for G in the case when the quantizing regions form a periodic tiling of n-dimensional space, in terms of the volumes and second moments of the Voronoi cells. As an application we show, extending earlier work of Kashyap and Neuhoff, that even a variable-rate three-dimensional quantizer based on the ``A15'' structure is still inferior to a quantizer based on the body-centered cubic lattice. We also determine the smallest covering radius of such a structure.
Cite
@article{arxiv.math/0207146,
title = {A Zador-Like Formula for Quantizers Based on Periodic Tilings},
author = {N. J. A. Sloane and Vinay A. Vaishampayan},
journal= {arXiv preprint arXiv:math/0207146},
year = {2016}
}
Comments
8 pages