Algebraic tools to build modulation schemes for fading channels

A unified framework is presented in order to build lattice constellations matched to both the Rayleigh fading channel and the Gaussian channel. The method encompasses the situations where the interleaving is done on the real components or on two-dimensional signals. In the latter case, a simple construction of lattices congruent to the densest binary lattices with respect to the Euclidean distance is proposed. It generalizes, in a sense to be clarified later, the structural construction proposed by Forney. These constellations are next combined with coset codes. The partitioning rules and the gain formula are similar to those used for the Gaussian channel.