We consider the multiuser successive refinement (MSR) problem, where the
users are connected to a central server via links with different noiseless
capacities, and each user wishes to reconstruct in a successive-refinement
fashion. An achievable region is given for the two-user two-layer case and it
provides the complete rate-distortion region for the Gaussian source under the
MSE distortion measure. The key observation is that this problem includes the
multiple description (MD) problem (with two descriptions) as a subsystem, and
the techniques useful in the MD problem can be extended to this case. We show
that the coding scheme based on the universality of random binning is
sub-optimal, because multiple Gaussian side informations only at the decoders
do incur performance loss, in contrast to the case of single side information
at the decoder. We further show that unlike the single user case, when there
are multiple users, the loss of performance by a multistage coding approach can
be unbounded for the Gaussian source. The result suggests that in such a
setting, the benefit of using successive refinement is not likely to justify
the accompanying performance loss. The MSR problem is also related to the
source coding problem where each decoder has its individual side information,
while the encoder has the complete set of the side informations. The MSR
problem further includes several variations of the MD problem, for which the
specialization of the general result is investigated and the implication is
discussed.Comment: 10 pages, 5 figures. To appear in IEEE Transaction on Information
Theory. References updated and typos correcte