Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 8414-8418 |
Seitenumfang | 5 |
Fachzeitschrift | IEEE Transactions on Information Theory |
Jahrgang | 70 |
Ausgabenummer | 11 |
Frühes Online-Datum | 8 Mai 2024 |
Publikationsstatus | Veröffentlicht - Nov. 2024 |
Abstract
40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter-Todd lattice K 12 for quantization, and estimated its second moment. Since then, all published lists identify K 12 as the best 12-dimensional lattice quantizer. Surprisingly, K 12 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.
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- Informatik (insg.)
- Information systems
- Informatik (insg.)
- Angewandte Informatik
- Sozialwissenschaften (insg.)
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in: IEEE Transactions on Information Theory, Jahrgang 70, Nr. 11, 11.2024, S. 8414-8418.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Glued lattices are better quantizers than K12
AU - Agrell, Erik
AU - Pook-Kolb, Daniel
AU - Allen, Bruce
N1 - Publisher Copyright: Authors Publisher Copyright: © 1963-2012 IEEE.
PY - 2024/11
Y1 - 2024/11
N2 - 40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter-Todd lattice K 12 for quantization, and estimated its second moment. Since then, all published lists identify K 12 as the best 12-dimensional lattice quantizer. Surprisingly, K 12 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.
AB - 40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter-Todd lattice K 12 for quantization, and estimated its second moment. Since then, all published lists identify K 12 as the best 12-dimensional lattice quantizer. Surprisingly, K 12 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.
KW - Block codes
KW - Coxeter–Todd lattice
KW - Generators
KW - glue vectors
KW - gluing theory
KW - lattice theory
KW - Lattices
KW - mean square error
KW - moment of inertia
KW - normalized second moment
KW - Physics
KW - product lattice
KW - quantization constant
KW - quantization error
KW - Reflection
KW - Symmetric matrices
KW - vector quantization
KW - Vectors
KW - Voronoi region
KW - Coxeter-Todd lattice
UR - http://www.scopus.com/inward/record.url?scp=85192789283&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2312.00481
DO - 10.48550/arXiv.2312.00481
M3 - Article
AN - SCOPUS:85192789283
VL - 70
SP - 8414
EP - 8418
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 11
ER -