论文标题
由复杂整数构建的更好的晶格量化器
Better Lattice Quantizers Constructed from Complex Integers
论文作者
论文摘要
本文从复杂的晶格的角度研究了低维量化器。我们采用Eisenstein Integers和Gaussian Integers来定义棋盘格晶格$ \ MATHCAL {E} _ {M} $和$ \ MATHCAL {G} _ {M} $。通过将其晶格基底部与各种形式的$ \ Mathcal {e} _ {M} $和$ \ Mathcal {G} _ {M} $ cosets链接，我们发现$ \ nathcal {e} _ {e} _ {m，2}^+$ lattices，基于$ lattiz $ 14 $ nive $ lattice $ lattice $ lattice， $ 18 $，$ 19 $，$ 22 $和$ 23 $。提出了广义棋盘格晶格的快速量化算法，以通过蒙特卡洛整合能够评估归一化的第二刻（NSM）。
This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices $\mathcal{E}_{m}$ and $\mathcal{G}_{m}$. By explicitly linking their lattice bases to various forms of $\mathcal{E}_{m}$ and $\mathcal{G}_{m}$ cosets, we discover the $\mathcal{E}_{m,2}^+$ lattices, based on which we report the best known lattice quantizers in dimensions $14$, $15$, $18$, $19$, $22$ and $23$. Fast quantization algorithms of the generalized checkerboard lattices are proposed to enable evaluating the normalized second moment (NSM) through Monte Carlo integration.
