A Deterministic Polynomial--Time Algorithm for Constructing a Multicast Coding Scheme for Linear Deterministic Relay Networks

We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the well-known multicast network coding scheme of Jaggi et al. to linear deterministic relay networks and is based on the notion of flow for a unicast session that was introduced by the authors in earlier work. We present randomized and deterministic polynomial--time versions of our algorithm and show that for a network with $g$ destinations, our deterministic algorithm can achieve the capacity in $\left\lceil \log(g+1)\right\rceil$ uses of the network.Comment: 12 pages, 2 figures, submitted to CISS 201

Edge-Cut Bounds on Network Coding Rates

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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43451/1/10922_2005_Article_9019.pd

Edge-Cut Bounds On Network Coding Rates

Abstract — Two bounds on network coding rates are reviewed that generalize edge-cut bounds on routing rates. The simpler bound is a bidirected cut-set bound which generalizes and improves upon a flow cut-set bound that is standard in networking. It follows that routing is rate-optimal if routing achieves the standard flow cut-set bound. The second bound improves on the cut-set bound, and it involves progressively removing edges from a network graph and checking whether certain strengthened dseparation conditions are satisfied. I