Parametric Lattices Are Better Quantizers in Dimensions 13 and 14

TL;DR

This paper introduces new lattice quantizers in 13 and 14 dimensions with lower normalized second moments, combining numerical and analytical optimization, and conjectures their optimality.

Contribution

It presents a novel construction method for lattice quantizers using glued products and parameter optimization, improving quantization efficiency in high dimensions.

Findings

Lower normalized second moments achieved in 13 and 14 dimensions

Construction method based on scaled glued product lattices

Identification of phase changes in lattice parameter space

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.