Multiuser Successive Refinement and Multiple Description Coding

TL;DR

This paper investigates multiuser successive refinement and multiple description coding, providing a complete rate-distortion region for Gaussian sources and revealing limitations of certain coding schemes in multiuser scenarios.

Contribution

It extends the understanding of multiuser successive refinement, showing the limitations of random binning and multistage coding, and relates the problem to multiple description coding with new insights.

Findings

Achievable region for two-user two-layer case with Gaussian sources.

Random binning is sub-optimal for multiple Gaussian side informations.

Multistage coding can cause unbounded performance loss in multiuser settings.

Abstract

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.