  This paper studies network information theory problems where the external
noise is Gaussian distributed. In particular, the Gaussian broadcast channel
with coherent fading and the Gaussian interference channel are investigated. It
is shown that in these problems, non-Gaussian code ensembles can achieve higher
rates than the Gaussian ones. It is also shown that the strong Shamai-Laroia
conjecture on the Gaussian ISI channel does not hold. In order to analyze
non-Gaussian code ensembles over Gaussian networks, a geometrical tool using
the Hermite polynomials is proposed. This tool provides a coordinate system to
analyze a class of non-Gaussian input distributions that are invariant over
Gaussian networks.
