Glued lattices are better quantizers than K₁₂

authored by

Erik Agrell, Daniel Pook-Kolb, Bruce Allen

Abstract

40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter&#x2013;Todd lattice <italic>K</italic>₁₂ for quantization, and estimated its second moment. Since then, all published lists identify <italic>K</italic>₁₂ as the best 12-dimensional lattice quantizer. Surprisingly, <italic>K</italic>₁₂ is not optimal: we construct two new 12-dimensional lattices with lower normalized second moments. The new lattices are obtained by gluing together products of two 6-dimensional lattices.

Organisation(s)

Institute of Gravitation Physics

External Organisation(s)

Chalmers University of Technology
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)

Type

Article

Journal

IEEE Transactions on Information Theory

Pages

1

No. of pages

1

ISSN

0018-9448

Publication date

08.05.2024

Publication status

E-pub ahead of print

Peer reviewed

Yes

ASJC Scopus subject areas

Information Systems, Computer Science Applications, Library and Information Sciences

Electronic version(s)

https://doi.org/10.48550/arXiv.2312.00481 (Access: Open)
https://doi.org/10.1109/TIT.2024.3398421 (Access: Open)