Tiling of Constellations
| Autor: | Maiara F. Bollauf, Øyvind Ytrehus |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Code (set theory) Computer Science - Information Theory Information Theory (cs.IT) Structure (category theory) ComputerApplications_COMPUTERSINOTHERSYSTEMS Data_CODINGANDINFORMATIONTHEORY Information theory Linear code Injective function Combinatorics Abelian group Group theory Mathematics Constellation Computer Science::Information Theory |
| Zdroj: | ISIT |
| DOI: | 10.48550/arxiv.2105.04253 |
| Popis: | Motivated by applications in reliable and secure communication, we address the problem of tiling (or partitioning) a finite constellation in $\mathbb{Z}_{2^{L}}^{n}$ 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. |
| Databáze: | OpenAIRE |
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