  We investigate whether uncoded schemes are optimal for Gaussian sources on
multiuser Gaussian channels. Particularly, we consider two problems: the first
is to send correlated Gaussian sources on a Gaussian broadcast channel where
each receiver is interested in reconstructing only one source component (or one
specific linear function of the sources) under the mean squared error
distortion measure; the second is to send correlated Gaussian sources on a
Gaussian multiple-access channel, where each transmitter observes a noisy
combination of the source, and the receiver wishes to reconstruct the
individual source components (or individual linear functions) under the mean
squared error distortion measure. It is shown that when the channel parameters
match certain general conditions, the induced distortion tuples are on the
boundary of the achievable distortion region, and thus optimal. Instead of
following the conventional approach of attempting to characterize the
achievable distortion region, we ask the question whether and how a match can
be effectively determined. This decision problem formulation helps to
circumvent the difficult optimization problem often embedded in region
characterization problems, and it also leads us to focus on the critical
conditions in the outer bounds that make the inequalities become equalities,
which effectively decouple the overall problem into several simpler
sub-problems. Optimality results previously unknown in the literature are
obtained using this novel approach. As a byproduct of the investigation, novel
outer bounds are derived for these two problems.
