Good lattice constellations for both Rayleigh fading and Gaussian channels

Recent work on lattices matched to the Rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency. We present a new family of lattice constellations, based on complex algebraic number fields, which have good performance on Rayleigh fading channels. So...

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Bibliographic Details
Published in:IEEE transactions on information theory 1996-03, Vol.42 (2), p.502-518
Main Authors: Boutros, J., Viterbo, E., Rastello, C., Belfiore, J.-C.
Format: Article
Language:English
Subjects:
Communications
Constellation diagram
Convolutional codes
Diversity methods
Fading
Gaussian channels
Information technology
Lattices
Multidimensional systems
Rayleigh channels
Satellites
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Summary:Recent work on lattices matched to the Rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency. We present a new family of lattice constellations, based on complex algebraic number fields, which have good performance on Rayleigh fading channels. Some of these lattices also present a reasonable packing density and thus may be used at the same time over a Gaussian channel. Conversely, we show that particular versions of the best lattice packings (D/sub 4/, E/sub 6/, E/sub 8/, K/sub 12/, /spl Lambda//sub 16/, /spl Lambda//sub 24/), constructed from totally complex algebraic cyclotomic fields, present better performance over the Rayleigh fading channel. The practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links. Some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.485720