Parametric Lattices Are Better Quantizers in Dimensions 13 and 14
Information Theory
2024-12-02 v1 Mathematical Physics
math.IT
Metric Geometry
math.MP
Abstract
New lattice quantizers with lower normalized second moments than previously reported are constructed in 13 and 14 dimensions and conjectured to be optimal. Our construction combines an initial numerical optimization with a subsequent analytical optimization of families of lattices, whose Voronoi regions are constructed exactly. The new lattices are constructed from glued products of previously known lattices, by scaling the component lattices and then optimizing the scale factors. A two-parameter family of lattices in 13 dimensions reveals an intricate landscape of phase changes as the parameters are varied.
Cite
@article{arxiv.2411.19250,
title = {Parametric Lattices Are Better Quantizers in Dimensions 13 and 14},
author = {Daniel Pook-Kolb and Erik Agrell and Bruce Allen},
journal= {arXiv preprint arXiv:2411.19250},
year = {2024}
}
Comments
16 pages, 7 figures