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

Erik Agrell; Daniel Pook-Kolb; Bruce Allen

doi:10.1109/tit.2024.3398421

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arXiv · 2312.00481

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

Erik Agrell·Daniel Pook-Kolb·Bruce Allen

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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.

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BibTeX RIS

Erik Agrell, Daniel Pook-Kolb, Bruce Allen. 2023-12-01. Glued lattices are better quantizers than $K_{12}$. https://doi.org/10.1109/tit.2024.3398421

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