  We experimentally investigate mutual information and generalized mutual
information for coherent optical transmission systems. The impact of the
assumed channel distribution on the achievable rate is investigated for
distributions in up to four dimensions. Single channel and wavelength division
multiplexing (WDM) transmission over transmission links with and without inline
dispersion compensation are studied. We show that for conventional WDM systems
without inline dispersion compensation, a circularly symmetric complex Gaussian
distribution is a good approximation of the channel. For other channels, such
as with inline dispersion compensation, this is no longer true and gains in the
achievable information rate are obtained by considering more sophisticated
four-dimensional (4D) distributions. We also show that for nonlinear channels,
gains in the achievable information rate can also be achieved by estimating the
mean values of the received constellation in four dimensions. The highest gain
for such channels is seen for a 4D correlated Gaussian distribution.
