论文标题
确切计算任意晶格的量化常数
Exact calculation of quantizer constants for arbitrary lattices
论文作者
论文摘要
我们提出了一种算法，用于具有已知对称组的晶格的Voronoi细胞的精确计算机辅助结构。我们的算法比线性地尺度更好，而面部总数则适用于12个以上的尺寸，而以前的方法无法实现。新算法应用于Coxeter-todd lattice $ k_ {12} $，以及从层压$ k_ {12} $获得的晶格家族。通过优化该家族，我们获得了新的最佳13维晶格量化器（在具有已发表的精确量化器常数的晶格中）。
We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond 12, which previous methods could not achieve. The new algorithm is applied to the Coxeter-Todd lattice $K_{12}$ as well as to a family of lattices obtained from laminating $K_{12}$. By optimizing this family, we obtain a new best 13-dimensional lattice quantizer (among the lattices with published exact quantizer constants).
