High-Dimensional Signal Compression: Lattice Point Bounds and Metric Entropy
This work addresses compression problems in high-dimensional signal processing, but it appears incremental as it refines classical methods for specific precision profiles.
The paper tackles worst-case signal compression under an ℓ² energy constraints with coordinate-dependent quantization precisions, reducing it to counting lattice points in a diagonal ellipsoid, and obtains explicit, dimension-dependent upper bounds on logarithmic codebook size using refined lattice point estimates.
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.