Trellis coding with asymmetric modulations

Through the asymmetric design of signal constellations, it often becomes possible to obtain a performance gain over conventional symmetric constellations combined with trellis coding. Attention is given to the joint design of n/(n+1) trellis codes and asymmetric 2 exp (n+1)-point signal constellations having no bandwidth expansion relative to an uncoded 2 exp n-point symmetric signal set. The asymptotic performance gains due to coding and asymmetry are explained in terms of the minimum free Euclidean distance of the trellis; examples are given which show the performance gain due to the asymmetry of the signal set. Since asymmetry does not affect bandwidth or power requirements, these improvements come at little or no cost.