Glued lattices are better quantizers than $K_{12}$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913402200260608 |
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| author | Agrell, Erik Pook-Kolb, Daniel Allen, Bruce |
| author_facet | Agrell, Erik Pook-Kolb, Daniel Allen, Bruce |
| contents | 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 6-dimensional lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00481 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Glued lattices are better quantizers than $K_{12}$ Agrell, Erik Pook-Kolb, Daniel Allen, Bruce Information Theory Mathematical Physics Metric Geometry 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 6-dimensional lattices. |
| title | Glued lattices are better quantizers than $K_{12}$ |
| topic | Information Theory Mathematical Physics Metric Geometry |
| url | https://arxiv.org/abs/2312.00481 |