Shaping gains using non-equiprobable signaling

The method presented by A.R. Calderbank and L.H. Ozarow (IEEE Trans. Inform. Theory, vol.36, p.726-40, July 1990) is extended to provide shape gains without resorting to high-dimensional constellations. The extended method accomplishes this by dividing the constellation into unequal sized constellations and then selecting these constellations on an equiprobable basis. This approach yields higher shaping gains than the method of Calderbank and Ozarow, with lower increase in peak-to-average power ratios. A design example which demonstrates the simplicity and power of the approach is provided. It is shown that, for very little complexity, shaping gains of 1 dB can be achieved