Common Reconstructions in the Successive Refinement Problem with Receiver Side Information
Abstract
We study a variant of the successive refinement problem with receiver side information where the receivers require identical reconstructions. We present general inner and outer bounds for the rate region for this variant and present a single-letter characterization of the admissible rate region for several classes of the joint distribution of the source and the side information. The characterization indicates that the side information can be fully used to reduce the communication rates via binning; however, the reconstruction functions can depend only on the G\'acs-K\"orner common randomness shared by the two receivers. Unlike existing (inner and outer) bounds to the rate region of the general successive refinement problem, the characterization of the admissible rate region derived for several settings of the variant studied requires only one auxiliary random variable. Using the derived characterization, we establish that the admissible rate region is not continuous in the underlying source source distribution even though the problem formulation does not involve zero-error or functional reconstruction constraints.
Cite
@article{arxiv.1611.05467,
title = {Common Reconstructions in the Successive Refinement Problem with Receiver Side Information},
author = {Badri N. Vellambi and Roy Timo},
journal= {arXiv preprint arXiv:1611.05467},
year = {2016}
}
Comments
37 pages, 8 figures. Some of the material in this paper was presented at the 2013 IEEE Information Theory Workshop in Seville, Spain, and the 2014 IEEEInternational Symposium on Information Theory in Honolulu, USA, 2014. This work was supported by the Australian Research Council Discovery Project DP120102123