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Fuchsian codes with arbitrarily high code rates
dc.contributor.author | Blanco Chacón, Iván |
dc.contributor.author | Hollanti, Camilla |
dc.contributor.author | Alsina Aubach, Montserrat |
dc.contributor.author | Remón Adell, Dionís |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-03-18T16:57:26Z |
dc.date.available | 2019-01-01T01:30:27Z |
dc.date.issued | 2016-01-01 |
dc.identifier.citation | Blanco, I., Hollanti, C., Alsina, M., Remón, D. Fuchsian codes with arbitrarily high code rates. "Journal of pure and applied algebra", 01 Gener 2016, vol. 220, núm. 1, p. 180-196. |
dc.identifier.issn | 0022-4049 |
dc.identifier.uri | http://hdl.handle.net/2117/84742 |
dc.description.abstract | Recently, Fuchsian codes have been proposed in Blanco-Chacon et al. (2014) [2] for communication over channels subject to additive white Gaussian noise (AWGN). The two main advantages of Fuchsian codes are their ability to compress information, i.e., high code rate, and their logarithmic decoding complexity. In this paper, we improve the first property further by constructing Fuchsian codes with arbitrarily high code rates while maintaining logarithmic decoding complexity. Namely, in the case of Fuchsian groups derived from quaternion algebras over totally real fields we obtain a code rate that is proportional to the degree of the base field. In particular, we consider arithmetic Fuchsian groups of signature (1; e) to construct explicit codes having code rate six, meaning that we can transmit six independent integers during one channel use. |
dc.format.extent | 17 p. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
dc.subject.lcsh | Fuchsian groups |
dc.subject.lcsh | Coding theory |
dc.subject.other | Time Block-Codes |
dc.subject.other | Domains |
dc.title | Fuchsian codes with arbitrarily high code rates |
dc.type | Article |
dc.subject.lemac | Fuchsian, Grups de |
dc.subject.lemac | Codificació, Teoria de la |
dc.contributor.group | Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
dc.identifier.doi | 10.1016/j.jpaa.2015.06.005 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::20 Group theory and generalizations |
dc.rights.access | Open Access |
local.identifier.drac | 16614114 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2012-33830/ES/AVANCES EN EL PROGRAMA DE LANGLANDS: ARITMETICA DE FORMAS AUTOMORFAS Y MODULARIDAD/ |
local.citation.author | Blanco, I.; Hollanti, C.; Alsina, M.; Remón, D. |
local.citation.publicationName | Journal of pure and applied algebra |
local.citation.volume | 220 |
local.citation.number | 1 |
local.citation.startingPage | 180 |
local.citation.endingPage | 196 |
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