Papers › Better Lattice Quantizers Constructed from Complex Integers
Better Lattice Quantizers Constructed from Complex Integers
Shanxiang Lyu, Zheng Wang, Cong Ling, Hao Chen
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This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices ℰₘ and 𝒢ₘ. By explicitly linking their lattice bases to various forms of ℰₘ and 𝒢ₘ 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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