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Lattice constellations and codes from quadratic number fields

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5 Author(s)
Pires da Nobrega Neto, T. ; Dept. de Matematica, Univ. Estadual Paulista, Sao Paulo, Brazil ; Interlando, J.C. ; Favareto, O.M. ; Elia, M.
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We 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 module 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

Published in:

Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 4 )

Date of Publication:

May 2001

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