Glued lattices are better quantizers than $K_{12}$

Author:

Erik Agrell, Daniel Pook-Kolb, Bruce Allen

Keyword:

Computer Science, Information Theory, Information Theory (cs.IT), Mathematical Physics (math-ph), Metric Geometry (math.MG)

journal:

date:

2023-12-01 00:00:00

Abstract

40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter-Todd lattice $K_{12}$ for quantization, and estimated its second moment. Since then, all published lists identify $K_{12}$ as the best 12-dimensional lattice quantizer. Surprisingly, $K_{12}$ is not optimal: we construct two new 12-dimensional lattices with lower normalized second moments. The new lattices are obtained by gluing together 6-dimensional lattices.

PDF: Glued lattices are better quantizers than $K_{12}$.pdf