  This paper is motivated by a sensor network on a correlated field where
nearby sensors share information, and can thus assist rather than interfere
with one another. A special class of two-user Gaussian interference channels
(IFCs) is considered where one of the two transmitters knows both the messages
to be conveyed to the two receivers (called the IFC with degraded message
sets). Both achievability and converse arguments are provided for this scenario
for a class of discrete memoryless channels with weak interference. For the
case of the Gaussian weak interference channel with degraded message sets,
optimality of Gaussian inputs is also shown, resulting in the capacity region
of this channel.
