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arXiv · 1407.2417

Strong Converse Theorems for Classes of Multimessage Multicast Networks: A Rényi Divergence Approach

Silas L. Fong·Vincent Y. F. Tan
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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 Rényi divergence.

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Silas L. Fong, Vincent Y. F. Tan. 2015-07-31. Strong Converse Theorems for Classes of Multimessage Multicast Networks: A Rényi Divergence Approach. https://doi.org/10.1109/tit.2016.2584082

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