Edge-Cut Bounds on Network Coding Rates
Gerhard Kramer,Serap A. Savari +1 more
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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.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.read more
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Network coding in undirected graphs is either very helpful or not helpful at all
TL;DR: In this paper, the authors show that even a small advantage over MCF can be amplified to yield a near-maximum possible gap, which is close to the best currently known upper bound, which follows from the connection between MCF and sparsest cuts.
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Alignment based Network Coding for Two-Unicast-Z Networks
TL;DR: In this article, a linear network coding algorithm for two-unicast-Z networks over directed acyclic graphs is presented, with interference alignment as one of its key ingredients.
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Generalized Cut-Set Bounds for Broadcast Networks
Amir Salimi,Tie Liu,Shuguang Cui +2 more
TL;DR: In this paper, a new set of network coding bounds for general broadcast networks is proposed, which combine the basic cuts of the network via a variety of set operations (not just the union) and are established via the submodularity of Shannon entropy.
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Beyond the Cut-Set Bound: Uncertainty Computations in Network Coding with Correlated Sources
TL;DR: In this paper, the authors introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, that results in bounds that are tighter than the corresponding cut-set bounds.
References
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