Lattice constellations and codes from quadratic number fields

Lattice constellations and codes from quadratic number fields

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 Eisenste...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 47; no. 4; pp. 1514 - 1527
Main Authors: Pires da Nobrega Neto, T., Interlando, J.C., Favareto, O.M., Elia, M., Palazzo, R.
Format: Journal Article
Language:English
Published: New York IEEE 01-05-2001
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Codes
Constellations
Coordinates
Gaussian
Information systems
Integers
Linear codes
Mathematical analysis
Modulation
Quadrature amplitude modulation
Vectors (mathematics)
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Summary: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.
Bibliography:ObjectType-Article-2
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ISSN:0018-9448
1557-9654
DOI:10.1109/18.923731