Strong Converse Theorems for Classes of Multimessage Multicast Networks: A R\'enyi Divergence Approach
Abstract
This paper establishes that the strong converse holds for some classes of discrete memoryless multimessage multicast networks (DM-MMNs) whose corresponding cut-set bounds are tight, i.e., coincide with the set of achievable rate tuples. The strong converse for these classes of DM-MMNs implies that all sequences of codes with rate tuples belonging to the exterior of the cut-set bound have average error probabilities that necessarily tend to one (and are not simply bounded away from zero). Examples in the classes of DM-MMNs include wireless erasure networks, DM-MMNs consisting of independent discrete memoryless channels (DMCs) as well as single-destination DM-MMNs consisting of independent DMCs with destination feedback. Our elementary proof technique leverages properties of the R\'enyi divergence.
Keywords
Cite
@article{arxiv.1407.2417,
title = {Strong Converse Theorems for Classes of Multimessage Multicast Networks: A R\'enyi Divergence Approach},
author = {Silas L. Fong and Vincent Y. F. Tan},
journal= {arXiv preprint arXiv:1407.2417},
year = {2016}
}
Comments
Submitted to IEEE Transactions on Information Theory, Jul 18, 2014. Revised on Jul 31, 2015