Optimization and Identification of Lattice Quantizers
Journal article, 2025
Lattices with minimal normalized second moments are designed using a new numerical optimization algorithm. Starting from a random lower-triangular generator matrix and applying stochastic gradient descent, all elements are updated towards the negative gradient, which makes it the most efficient algorithm proposed so far for this purpose. A graphical illustration of the theta series, called theta image, is introduced and shown to be a powerful tool for converting numerical lattice representations into their underlying exact forms. As a proof of concept, optimized lattices are designed in dimensions up to 16. In all dimensions, the algorithm converges to either the previously best known lattice or a better one. The dual of the 15-dimensional laminated lattice is conjectured to be optimal in its dimension and its exact normalized second moment is computed.
lattice quantization
lattice design
Algorithm
theta series
vector quantization
stochastic gradient descent
moment of inertia
normalized second moment
mean square error
theta image
laminated lattice
numerical optimization
Voronoi region
quantization constant
Author
Erik Agrell
Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks
Max Planck Society
Daniel Pook-Kolb
University of Hanover
Bruce Allen
University of Hanover
IEEE Transactions on Information Theory
0018-9448 (ISSN) 1557-9654 (eISSN)
Vol. 71 8 6490-6501Subject Categories (SSIF 2025)
Probability Theory and Statistics
Condensed Matter Physics
DOI
10.1109/TIT.2025.3565218