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.

翻译：我们研究在$\ell^2$能量约束下，具有坐标依赖量化精度的最坏情况信号压缩问题。该压缩问题被简化为计算对角椭球中的格点数目。在均衡精度配置下，我们得到了代码簿对数大小的显式、依赖于维度的上界。该分析利用Olenko的均匀贝塞尔界和显式阿贝尔求和，对Landau经典的格点估计进行了改进。