Better Lattice Quantizers Constructed from Complex Integers

2022/04/03 by Shanxiang Lyu, Lyu, Shanxiang, Wang, Zheng +4 · 2 citations
Computer Science · Medicine · #Advanced Data Compression Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Medical Imaging Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2204.01105

openalex publication_date 2022/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices E_m and G_m. By explicitly linking their lattice bases to various forms of E_m and G_m cosets, we discover the 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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