Multidimensional Signal Sets Through the Shell Construction for Parallel Channels

Abstract

The design of efficient multidimensional signal sets has gained importance with the development of coset codes. We derive a procedure to send r bits on M parallel channels. A decomposition of the best constellation in [formulae omitted] is given in terms of the cross-products of lower dimensional shells of points. The proposed scheme can be used with good known coset codes to provide an alternate method of coded modulation. Our results indicate that we can get good shaping gains for low encoder complexity. The method is also generalized for channels with unequal gains. We also find a significant performance advantage at fixed shaping gain, in certain cases, with respect to the recent Voronoi Constellations in terms of peak-to-average power and constellation expansion. © 1992 IEEE