Rate Distortion With Side-Information at Many Decoders

We present an achievable rate region for the multistage successive-refinement problem with side-information. We also present an upper bound for the rate-distortion function for lossy source coding with side-information at many decoders. 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” (IEEE Trans. Inf. Theory, 1985). We give a counterexample to Heegard and Berger´s result.