A Zador-Like Formula for Quantizers Based on Periodic Tilings
<|reference_start|>A Zador-Like Formula for Quantizers Based on Periodic Tilings: 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.<|reference_end|>
@article{sloane2002a,
    title={A Zador-Like Formula for Quantizers Based on Periodic Tilings},
    author={N. J. A. Sloane, Vinay A. Vaishampayan},
    journal={IEEE Trans. Information Theory 48 (2002), 3138-3140},
    year={2002},
    doi={10.1109/TIT.2002.805086},
    archivePrefix={arXiv},
    eprint={math/0207146},
    primaryClass={math.CO cs.IT math.IT}
}