  An important notion of common information between two random variables is due
to Wyner. In this paper, we derive a lower bound on Wyner's common information
for continuous random variables. The new bound improves on the only other
general lower bound on Wyner's common information, which is the mutual
information. We also show that the new lower bound is tight for the so-called
"Gaussian channels" case, namely, when the joint distribution of the random
variables can be written as the sum of a single underlying random variable and
Gaussian noises. We motivate this work from the recent variations of Wyner's
common information and applications to network data compression problems such
as the Gray-Wyner network.
