New results on Gaussian interference channel problem and multiple description 
problem are discussed. In Gaussian interference channel problem, we show 
that the existing outer bounds can in fact be
arbitrarily loose in some parameter ranges, and  by deriving new
outer bounds, we show that a simplified Han-Kobayashi type scheme
can achieve to within a single bit the capacity for all values of
the channel parameters. We also show that the scheme is
asymptotically optimal at certain high SNR regimes. Using our
results, we provide a natural generalization of the point-to-point
classical notion of degrees of freedom to interference-limited
scenarios. In multiple description problem, we investigate
L multiple descriptions of a vector Gaussian source for
individual and central receivers. The sum rate of
the descriptions with covariance distortion measure constraints,
in a positive semidefinite ordering, is exactly characterized. For
two descriptions, the entire rate region is characterized.
The key component of the solution is a novel information-theoretic
inequality that is used to lower bound the achievable multiple
description rates. We show that jointly Gaussian descriptions are 
optimal in achieving the limiting rates. We also show the robustness 
of this description scheme: the distortions achieved are no larger when used to 
describe any non-Gaussian source with the same covariance matrix.