Hyperbolic Geometrically Uniform Codes and Ungerboeck Partitioning on the Double Torus

• Autor(a) principal: Gomes, Eduardo Michel Vieira
• Data de Publicação: 2022
• Outros Autores: de Carvalho, Edson Donizete [UNESP], Martins, Carlos Alexandre Ribeiro, Soares, Waldir Silva, da Silva, Eduardo Brandani
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.3390/sym14030449; http://hdl.handle.net/11449/230651
• topic: double torus; Fuchsian groups; geometrically uniform codes; hyperbolic geometry; signal constellations; Ungerboeck partitioning

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.