Better Lattice Quantizers Constructed from Complex Integers

arXiv2204.01105MaRDI QIDQ6395533

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Publication date: 3 April 2022

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.

Has companion code repository: https://github.com/shx-lyu/latticequantizer

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