Better Lattice Quantizers Constructed from Complex Integers

04/03/2022

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by   Shanxiang Lyu, et al.

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Real-valued lattices and complex-valued lattices are mutually convertible, thus we can take advantages of algebraic integers to defined good lattice quantizers in the real-valued domain. In this paper, we adopt complex integers to define generalized checkerboard lattices, especially ℰ_m and ℰ_m^+ defined by Eisenstein integers. Using ℰ_m^+, we report the best lattice quantizers in dimensions 14, 18, 20, and 22. Their product lattices with integers ℤ also yield better quantizers in dimensions 15, 19, 21, and 23. The Conway-Sloane type fast decoding algorithms for ℰ_m and ℰ_m^+ are given.