Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1 |
| Seitenumfang | 1 |
| Fachzeitschrift | IEEE Transactions on Information Theory |
| Frühes Online-Datum | 8 Mai 2024 |
| Publikationsstatus | Elektronisch veröffentlicht (E-Pub) - 8 Mai 2024 |
Abstract
40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter–Todd lattice <italic>K</italic>12 for quantization, and estimated its second moment. Since then, all published lists identify <italic>K</italic>12 as the best 12-dimensional lattice quantizer. Surprisingly, <italic>K</italic>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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in: IEEE Transactions on Information Theory, 08.05.2024, S. 1.
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
PY - 2024/5/8
Y1 - 2024/5/8
N2 - 40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter–Todd lattice K12 for quantization, and estimated its second moment. Since then, all published lists identify K12 as the best 12-dimensional lattice quantizer. Surprisingly, K12 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 K12 for quantization, and estimated its second moment. Since then, all published lists identify K12 as the best 12-dimensional lattice quantizer. Surprisingly, K12 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
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
SP - 1
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
ER -