Rate-Distortion with Side-Information at Many Receivers

We present an inner bound for the admissible rate region of the t-stage successive refinement problem with side information, and we present an upper bound for the rate-distortion function for lossy source coding with multiple receivers and side information. A single-letter characterisation of this rate-distortion function is a long standing open problem in multi-terminal information theory, 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. Inform. Theory, 1985. We give a counterexample to Heegard and Berger’s result, and we develop our new upper bound as a corollary to our inner bound for the successive refinement problem with side information. Index Terms Source coding with receiver side information, rate-distortion function, successive refinement, complementary delivery, side information scalable source coding