On the multimessage capacity region for undirected ring networks

  • Authors:
  • S. M. Sadegh Tabatabaei Yazdi;Serap A. Savari;Gerhard Kramer;Kelli Carlson;Farzad Farnoud

  • Affiliations:
  • Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX;Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX;Department of Electrical Engineering, University of Southern California, Los Angeles, CA and Bell Labs, Alcatel-Lucent;Department of Mathematics, University of Michigan, Ann Arbor, MI;Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2010

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Abstract

The "Japanese" theorem is extended to multiple multicast sessions in an arbitrary network to characterize the routing capacity region by the intersection of an infinite collection of half-spaces. An elimination technique is developed to simplify this infinite description into a finite one based upon the shortest routing paths and trees in the network graph. This result is used as a step in providing the capacity regions for two multimessage multicast problems on undirected ring networks; in the first case only unicast and broadcast sessions are considered, and in the second case multicast sessions where the source and destination vertices form lines of adjacent vertices are studied. Network coding is generally necessary to achieve network capacity, but for our multimessage multicast problems, new arguments are used to demonstrate that routing can achieve network coding bounds.