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Better Lattice Quantizers Constructed from Complex Integers (2204.01105v3)
Published 3 Apr 2022 in cs.IT and math.IT
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.