Optimization and Identification of Lattice Quantizers
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| Titel: | Optimization and Identification of Lattice Quantizers |
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| Autoren: | Agrell, Erik, 1965, Pook-Kolb, Daniel, Allen, Bruce |
| Quelle: | IEEE Transactions on Information Theory. 71(8):6490-6501 |
| Schlagwörter: | mean square error, lattice design, numerical optimization, moment of inertia, theta series, Algorithm, stochastic gradient descent, theta image, vector quantization, normalized second moment, laminated lattice, quantization constant, lattice quantization, Voronoi region |
| Beschreibung: | 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. |
| Dateibeschreibung: | electronic |
| Zugangs-URL: | https://research.chalmers.se/publication/546282 https://research.chalmers.se/publication/546282/file/546282_Fulltext.pdf |
| Datenbank: | SwePub |
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Nájsť tento článok vo Web of Science | Abstract: | 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. |
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| ISSN: | 00189448 15579654 |
| DOI: | 10.1109/TIT.2025.3565218 |