Edge-Cut Bounds on Network Coding Rates

  • Authors:
  • Gerhard Kramer;Serap A. Savari

  • Affiliations:
  • Aff1 Aff3;Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, USA

  • Venue:
  • Journal of Network and Systems Management
  • Year:
  • 2006

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Abstract

Active networks are network architectures with processors that are capable of executing code carried by the packets passing through them. A critical network management concern is the optimization of such networks and tight bounds on their performance serve as useful design benchmarks. A new bound on communication rates is developed that applies to network coding, which is a promising active network application that has processors transmit packets that are general functions, for example a bit-wise XOR, of selected received packets. The bound generalizes an edge-cut bound on routing rates by progressively removing edges from the network graph and checking whether certain strengthened d-separation conditions are satisfied. The bound improves on the cut-set bound and its efficacy is demonstrated by showing that routing is rate-optimal for some commonly cited examples in the networking literature.