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A Zador-Like Formula for Quantizers Based on Periodic Tilings

N. J. A. Sloane·Vinay A. Vaishampayan
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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.

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N. J. A. Sloane, Vinay A. Vaishampayan. 2002-07-17. A Zador-Like Formula for Quantizers Based on Periodic Tilings. https://doi.org/10.1109/tit.2002.805086

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