Tiling of Constellations
Information Theory
2021-05-13 v2 math.IT
Abstract
Motivated by applications in reliable and secure communication, we address the problem of tiling (or partitioning) a finite constellation in by subsets, in the case that the constellation does not possess an abelian group structure. The property that we do require is that the constellation is generated by a linear code through an injective mapping. The intrinsic relation between the code and the constellation provides a sufficient condition for a tiling to exist. We also present a necessary condition. Inspired by a result in group theory, we discuss results on tiling for the particular case when the finer constellation is an abelian group as well.
Keywords
Cite
@article{arxiv.2105.04253,
title = {Tiling of Constellations},
author = {Maiara F. Bollauf and Øyvind Ytrehus},
journal= {arXiv preprint arXiv:2105.04253},
year = {2021}
}