Details
| Original language | English |
|---|---|
| Pages (from-to) | 1 |
| Number of pages | 1 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 70 |
| Issue number | 11 |
| Early online date | 8 May 2024 |
| Publication status | Published - Nov 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.
Keywords
- Block codes, Coxeter–Todd lattice, Generators, glue vectors, gluing theory, lattice theory, Lattices, mean square error, moment of inertia, normalized second moment, Physics, product lattice, quantization constant, quantization error, Reflection, Symmetric matrices, vector quantization, Vectors, Voronoi region
ASJC Scopus subject areas
- Computer Science(all)
- Information Systems
- Computer Science(all)
- Computer Science Applications
- Social Sciences(all)
- Library and Information Sciences
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In: IEEE Transactions on Information Theory, Vol. 70, No. 11, 11.2024, p. 1.
Research output: Contribution to journal › Article › Research › 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 - 2024/11
Y1 - 2024/11
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
VL - 70
SP - 1
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 11
ER -