A spectral analysis of nonequiprobable signalling.

Abstract

In this thesis, a review of the fundamentals of the shaping codes and trellis shaping methods is provided. This analysis begins with a consideration of the spectral properties of memoryless modulation producing nonequiprobable signalling. Then, spectral properties of two examples of signals from shaping codes and sixteen examples of trellis shaping are numerically analyzed. It was found that the statistics of the signal points affect the power spectrum of the coded output signal. Yet, if certain symmetry rules are obeyed in design of the transmission system, such that a 90$\sp\circ$ rotational symmetric constellation (180$\sp\circ$ symmetric for QAM signalling) is combined with any linear error correcting code, the power spectrum of the output signal sequence can be made invariant to the changes in the statistics of the signal points. These symmetry rules relate to the geometrical symmetry of the signal points. These symmetry rules relate to the geometrical symmetry of the signal constellation and to the linearity of the codes used in communications system. Consequently, it has been verified that shaping gain can be achieved by nonequiprobable signalling without an expansion in the transmission bandwidth. (Abstract shortened by UMI.)