Nonequiprobable Signaling on the Gaussian Channel

Many signaling schemes for the Gaussian channel are based on finite-dimensional lattices. The signal constellation consists of all lattice points within a region and the shape of this region determines the average signal power. Spherical signal constellations minimize average signal power, and in the limit as N→∞ the shape gain of the N-sphere over the N-cube approaches πe/6≈ 1.53 dB. A nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension. A signal constellation ft is partitioned into T subconstellations Ω0, …, ΩT-1of equal size by scaling a basic region ℛ. Signal points in the same subconstellation are used equiprobably, and a shaping code selects the subconstellation ft, with frequency fi. Shaping codes make it possible to achieve any desired fractional bit rate. We compare our schemes with equiprobable signaling schemes based on Voronoi regions of multidimensional lattices. For comparable shape gain and constellation expansion ratio, the peak to average power ratio of our schemes is superior. Furthermore a simple table look-up is all that is required to address points in our constellations. This is not the case for Voronoi constellations where the complexity of addressing signal points is governed by the complexity of decoding the lattice. We also show that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework. © 1990 IEEE

Duke Scholars

Author Robert Calderbank Computer Science