We present a new inner bound for the rate region of the t-stage
successive-refinement problem with side-information. We also present a new
upper bound for the rate-distortion function for lossy-source coding with
multiple decoders and side-information. Characterising this rate-distortion
function is a long-standing open problem, and it is widely believed that the
tightest upper bound is provided by Theorem 2 of Heegard and Berger's paper
"Rate Distortion when Side Information may be Absent", \emph{IEEE Trans.
Inform. Theory}, 1985. We give a counterexample to Heegard and Berger's result.Comment: 36 pages. Submitted to IEEE Transactions on Information Theory. In
proc. ISIT 2010