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.
theta image
mean square error
vector quantization
lattice theory
quantization error
quantization constant
gluing theory
moment of inertia
Voronoi region
lattice quantization
parametric lattice
normalized second moment
lattice design
Author
Daniel Pook-Kolb
University of Hanover
Max Planck Society
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