Glued lattices are better quantizers than K 12
Journal article, 2024
40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter–Todd lattice K12 for quantization, and estimated its second moment. Since then, all published lists identify K12 as the best 12-dimensional lattice quantizer. Surprisingly, K12 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.
Block codes
vector quantization
moment of inertia
glue vectors
Reflection
normalized second moment
Voronoi region
quantization constant
Generators
Physics
Lattices
Coxeter–Todd lattice
gluing theory
mean square error
product lattice
Symmetric matrices
Vectors
lattice theory
quantization error
Author
Erik Agrell
Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks
Daniel Pook-Kolb
Max Planck Society
Bruce Allen
Max Planck Society
IEEE Transactions on Information Theory
0018-9448 (ISSN) 1557-9654 (eISSN)
Vol. 70 11 8414-8418Subject Categories
Probability Theory and Statistics
DOI
10.1109/TIT.2024.3398421