Calderbank, AR; Ozarow, LH, *Non-equiprobable signaling on the Gaussian channel*
(1990),
pp. 145- .
**Abstract:**

*Summary form only given, as follows. Many signaling schemes for the Gaussian channel are based on finite-dimensional lattices. The signal constellation consists of all lattice points within a region R, and the shape of this region determines the average signal power. In the limit as N → ∞, the shape gain the N-sphere over the N-cube approaches πe/6 = 1.53 dB. It is shown that the full asymptotic shape gain can be realized in any fixed dimension by nonequiprobable signaling. Shaping schemes that achieve a significant fraction of the available asymptotic shaping gain are described. The peak-to-average-power ratio of these schemes is superior to that of equiprobable signaling schemes based on Voronoi regions of multidimensional lattices. The new shaping schemes admit a simple staged demodulation procedure.*