On Signal Constellations Over Eisenstein Integers
Abdul Hadi, Uha Isnaini, Indah Emilia Wijayanti, Martianus Frederic Ezerman · IEEE Transactions on Information Theory · 2025
We propose constructions of signal constellations over quotient rings of Eisenstein integers equipped with the Euclidean, square Euclidean, and hexagonal distances as a generalization of those over Eisenstein integer fields. By set partitioning, we effectively divide the quotient ring of Eisenstein integers into equal-sized subsets for distinct encoding. Unlike in Eisenstein integer fields where partitioning is not feasible due to structural limitations, we can partition the quotient rings into additive subgroups in such a way that the minimum squared Euclidean and hexagonal distances of each subgroup are strictly larger than in the original set. This technique facilitates multilevel coding and enhances signal constellation efficiency.