High-Dimensional Signal Compression: Lattice Point Bounds and Metric Entropy
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915913487351808 |
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| author | Iosevich, A. Vagharshakyan, A. Wyman, E. |
| author_facet | Iosevich, A. Vagharshakyan, A. Wyman, E. |
| contents | We study worst-case signal compression under an $\ell^2$ energy constraint, with coordinate-dependent quantization precisions. The compression problem is reduced to counting lattice points in a diagonal ellipsoid. Under balanced precision profiles, we obtain explicit, dimension-dependent upper bounds on the logarithmic codebook size. The analysis refines Landau's classical lattice point estimates using uniform Bessel bounds due to Olenko and explicit Abel summation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03178 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High-Dimensional Signal Compression: Lattice Point Bounds and Metric Entropy Iosevich, A. Vagharshakyan, A. Wyman, E. Information Theory Numerical Analysis Number Theory 94A29 (Primary) 41A46, 11P21 (Secondary) We study worst-case signal compression under an $\ell^2$ energy constraint, with coordinate-dependent quantization precisions. The compression problem is reduced to counting lattice points in a diagonal ellipsoid. Under balanced precision profiles, we obtain explicit, dimension-dependent upper bounds on the logarithmic codebook size. The analysis refines Landau's classical lattice point estimates using uniform Bessel bounds due to Olenko and explicit Abel summation. |
| title | High-Dimensional Signal Compression: Lattice Point Bounds and Metric Entropy |
| topic | Information Theory Numerical Analysis Number Theory 94A29 (Primary) 41A46, 11P21 (Secondary) |
| url | https://arxiv.org/abs/2604.03178 |