Lattice constellations and codes from quadratic number fields

dc.contributorUniversidade Estadual Paulista (UNESP)
dc.creatorPires Da Nóbrega Neto, T.
dc.creatorInterlando, J. C.
dc.creatorFavareto, O. M.
dc.creatorElia, M.
dc.creatorPalazzo R., Jr
dc.date2014-05-27T11:20:16Z
dc.date2016-10-25T18:17:02Z
dc.date2014-05-27T11:20:16Z
dc.date2016-10-25T18:17:02Z
dc.date2001-05-01
dc.date.accessioned2017-04-06T00:59:30Z
dc.date.available2017-04-06T00:59:30Z
dc.identifierIEEE Transactions on Information Theory, v. 47, n. 4, p. 1514-1527, 2001.
dc.identifier0018-9448
dc.identifierhttp://hdl.handle.net/11449/66509
dc.identifierhttp://acervodigital.unesp.br/handle/11449/66509
dc.identifier10.1109/18.923731
dc.identifierWOS:000168790600017
dc.identifier2-s2.0-0035334579
dc.identifierhttp://dx.doi.org/10.1109/18.923731
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/888069
dc.descriptionWe propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.
dc.languageeng
dc.relationIEEE Transactions on Information Theory
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectAlgebraic decoding
dc.subjectEuclidean domains
dc.subjectLattices
dc.subjectLinear codes
dc.subjectMannheim distance
dc.subjectNumber fields
dc.subjectSignal sets matched to groups
dc.subjectAlgorithms
dc.subjectCodes (symbols)
dc.subjectDecoding
dc.subjectError analysis
dc.subjectLinearization
dc.subjectMaximum likelihood estimation
dc.subjectMaximum principle
dc.subjectNumber theory
dc.subjectQuadratic programming
dc.subjectQuadrature amplitude modulation
dc.subjectTwo dimensional
dc.subjectVector quantization
dc.subjectEinstein-Jacobi integers
dc.subjectGaussian integers
dc.subjectHamming distance
dc.subjectLattice codes
dc.subjectLattice constellations
dc.subjectManhattan metric modulo
dc.subjectMannheim metric
dc.subjectMaximum distance separable
dc.subjectQuadratic number fields
dc.subjectInformation theory
dc.titleLattice constellations and codes from quadratic number fields
dc.typeOtro


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