Better Lattice Quantizers Constructed from Complex Integers

Shanxiang Lyu; Zheng Wang; Cong Ling; Hao Chen

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arXiv · 2204.01105

Better Lattice Quantizers Constructed from Complex Integers

Shanxiang Lyu·Zheng Wang·Cong Ling·Hao Chen

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Abstract

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.

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Shanxiang Lyu, Zheng Wang, Cong Ling, Hao Chen. 2022-04-03. Better Lattice Quantizers Constructed from Complex Integers. https://arxiv.org/abs/2204.01105

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