Parametric Lattices Are Better Quantizers in Dimensions 13 and 14
Journal article, 2026
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.
lattice quantization
moment of inertia
quantization constant
lattice theory
vector quantization
parametric lattice
theta image
gluing theory
quantization error
Voronoi region
lattice design
mean square error
normalized second moment
Author
Daniel Pook-Kolb
Max Planck Society
University of Hanover
Erik Agrell
Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks
Bruce Allen
University of Hanover
Max Planck Society
IEEE Transactions on Information Theory
0018-9448 (ISSN) 1557-9654 (eISSN)
Vol. In PressSubject Categories (SSIF 2025)
Computer Sciences
DOI
10.1109/TIT.2026.3721285