Title :
Lattice constellations and codes from quadratic number fields
Author :
Da Nóbrega Neto, Trajano Pires ; Interlando, J. Carmelo ; Favareto, Osvaldo Milare ; Elia, Michele ; Palazzo, Reginaldo, Jr.
Author_Institution :
Dept. de Matematica, Univ. Estadual Paulista, Sao Paulo, Brazil
fDate :
5/1/2001 12:00:00 AM
Abstract :
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
Keywords :
linear codes; maximum likelihood decoding; modulation coding; quadrature amplitude modulation; 2D grid; Eisenstein-Jacobi integers; Gaussian integers; Hamming distance; Manhattan metric module; Mannheim metric; Mannheim weight errors; Mannheim-metric codes; QAM-type constellations; coded modulation; decoding algorithms; integer rings; lattice codes; lattice constellations; linear codes; maximum likelihod decoding; maximum-distance separable codes; quadratic number fields; quadrature amplitude modulation; rational numbers; transmitted code vector; Amplitude modulation; Constellation diagram; Euclidean distance; Hamming distance; Lattices; Linear code; Maximum likelihood decoding; Modulation coding; Quadrature amplitude modulation; Two dimensional displays;
Journal_Title :
Information Theory, IEEE Transactions on