On Product Distance of Lattice Code over a Biquadratic Number Field
Abstract
Lattice code is a type of error correcting codes composed of the image of embedding map of an integral ideal in a certain algebraic number field with a bilinear form. In a mobile communication, transmitted signals are attenuated by phenomenon called fading, and the Rayleigh fading of multi-path radio wave is one of important and essential type of fading. Some lattice codes are applicable in order to mitigate the influence of the fading and to extract the most feasible source information from the received signal.
The minimum product distance is one of key indicators of lattice code along with the modulation diversity. In this paper, we show some experimental results on the minimum product distance for some lattices of prime ideal in a composition fields of two real quadratic fields using a free formula manipulation system, PARI/GP.
References
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E. Bayer-Fluckiger, F. Oggier, E. Viterbo, “New algebraic constructions of rotated Znlattice constellations for the Rayleigh fading channel”, IEEE Trans. on Information Theory, vol. 50, no 4, 2004, pp. 702-714.
F. Oggier, “Algebraic Methods for Channel Coding”, THESE ` No 3182, Ecole Polytechnique F ´ ed´ erale de Lausanne, 2005, 5, Mar. 2014; ´ http://biblion.epfl.ch/EPFL/theses/2005/3182/3182_abs.pdf
PARI/GP Home, 26, Nov. 2014; http://pari.math.u-bordeaux.fr/
