  We consider the Cascade and Triangular rate-distortion problems where the
same side information is available at the source node and User 1, and the side
information available at User 2 is a degraded version of the side information
at the source node and User 1. We characterize the rate-distortion region for
these problems. For the Cascade setup, we showed that, at User 1, decoding and
re-binning the codeword sent by the source node for User 2 is optimum. We then
extend our results to the Two way Cascade and Triangular setting, where the
source node is interested in lossy reconstruction of the side information at
User 2 via a rate limited link from User 2 to the source node. We characterize
the rate distortion regions for these settings. Complete explicit
characterizations for all settings are also given in the Quadratic Gaussian
case. We conclude with two further extensions: A triangular source coding
problem with a helper, and an extension of our Two Way Cascade setting in the
Quadratic Gaussian case.
