Multicast throughput order of network coding in wireless ad-hoc networks

  • Authors:
  • Shirish Karande;Zheng Wang;Hamid R. Sadjadpour;J. J. Garcia-Luna-Aceves

  • Affiliations:
  • Philips Research Bangalore, Ulsoor, Bangalore, India;Department of Electrical Engineering, University of California, Santa Cruz, Santa Cruz, CA;Department of Electrical Engineering, University of California, Santa Cruz, Santa Cruz, CA;Computer Engineering, University of California, Santa Cruz, Santa Cruz, CA and Palo Alto Research Center, Palo Alto, CA

  • Venue:
  • SECON'09 Proceedings of the 6th Annual IEEE communications society conference on Sensor, Mesh and Ad Hoc Communications and Networks
  • Year:
  • 2009

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Abstract

We show that network coding (NC) does not provide any order gain in the multicast capacity of random wireless ad hoc networks. We consider a network with n nodes distributed uniformly in a unit square, with each node acting as a source for independent information to be sent to a multicast group consisting of m randomly chosen destinations. We show that, in the presence of NC, the per-session capacity under the protocol model has a tight bound of Θ(1/√mnlog(n)) when m = O(n/log(n)) and Θ(1/n) when m = Ω(n/log(n)). Furthermore, we show that the per-session capacity under the physical model has a tight bound of Θ(1/√mn) when m = O(n/(log(n))3), and Θ(1/n) when m = Ω(n/log(n)). Prior work has shown that these same order bounds are achievable utilizing only traditional store-and-forward methods.