On the rate-distortion region for multiple descriptions

The problem of source coding with multiple descriptions (the multiple descriptions problem) was first posed by Gersho, Witsenhausen, Wolf, Wyner, Ziv and Ozarow at the 1979 IEEE Information Theory Workshop. Since then, this problem has been extensively studied. El Gamal and Cover (1982) obtained an inner bound on the rate-distortion region for multiple descriptions, and showed that it is tight for the case of deterministic distortion measures. Ozarow (1980) showed that this inner bound is also tight for the Gaussian source with the square error distortion. Furthermore, Ahlswede (1985), Zhang and Berger (1987) showed that the El Gamal-Cover region is tight for the case of no excess rate for the joint description. In the excess rate case, Zhang and Berger showed by a counterexample that the El Gamal-Cover region is not tight in general. How to establish the rate-distortion region for multiple descriptions is still open. It is one of the well known hard problems in multiuser information theory. In this paper, we study the problem of source coding with multiple descriptions for a discrete memoryless source