  We consider a rate-distortion problem with side information at multiple
decoders. Several upper and lower bounds have been proposed for this general
problem or special cases of it. We provide an upper bound for general instances
of this problem, which takes the form of a linear program, by utilizing random
binning and simultaneous decoding techniques and compare it with the existing
bounds. We also provide a lower bound for the general problem, which was
inspired by a linear-programming lower bound for index coding, and show that it
subsumes most of the lower bounds in literature. Using these upper and lower
bounds, we explicitly characterize the rate-distortion function of a problem
that can be seen as a Gaussian analogue of the "odd-cycle" index coding
problem.
