Hyperbolic Geometrically Uniform Codes and Ungerboeck Partitioning on the Double Torus

Autor:	Eduardo Michel Vieira Gomes, Edson Donizete de Carvalho, Carlos Alexandre Ribeiro Martins, Waldir Silva Soares, Eduardo Brandani da Silva
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	geometrically uniform codes hyperbolic geometry Ungerboeck partitioning double torus Fuchsian groups signal constellations Mathematics QA1-939
Zdroj:	Symmetry, Vol 14, Iss 3, p 449 (2022)
Druh dokumentu:	article
ISSN:	2073-8994
DOI:	10.3390/sym14030449
Popis:	Current research builds labelings for geometrically uniform codes on the double torus through tiling groups. At least one labeling group was provided for all of the 11 regular tessellations on the double torus, derived from triangular Fuchsian groups, as well as extensions of these labeling groups to generate new codes. An important consequence is that such techniques can be used to label geometrically uniform codes on surfaces with greater genera. Furthermore, partitioning chains are constructed into geometrically uniform codes using soluble groups as labeling, which in some cases results in an Ungerboeck partitioning for the surface. As a result of these constructions, it is demonstrated that, as in Euclidean spaces, modulation and encoding can be combined in a single step in hyperbolic space.
Databáze:	Directory of Open Access Journals
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