Edge-Cut Bounds on Network Coding Rates
Gerhard Kramer,Serap A. Savari +1 more
TLDR
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
Citations
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Journal ArticleDOI
The Complexity of Network Coding With Two Unit-Rate Multicast Sessions
TL;DR: This paper proves that for the 2-URMS networks, the solvability can be determined with time O(|E|); an optimal solution can be obtained in polynomial time and the number of encoding links required to achieve a solution is upper-bounded by max{3,2N - 2}.
Proceedings ArticleDOI
An information-theoretic meta-theorem on edge-cut bounds
Sudeep Kamath,Pramod Viswanath +1 more
TL;DR: It is demonstrated that in these very cases, such edge-cut based bounds are actually `close' to fundamental yielding an approximate characterization of the capacity region for these problems, and suggests a meta-theorem: if there is inherent symmetry either in the network connectivity or in the traffic pattern, then edge- cut bounds are near-fundamental and flows approximately achieve capacity.
Proceedings ArticleDOI
The Capacity Region of a Collection of Multicast Sessions in an Undirected Ring Network
TL;DR: It is demonstrated that routing is rate optimal in this case using new extensions to progressive d-separating edge set bounds.
Proceedings ArticleDOI
Beyond the cut-set bound: Uncertainty computations in network coding with correlated sources
TL;DR: A new technique for proving converses for the problem of transmission of correlated sources in networks, which results in bounds that are tighter than the corresponding cut-set bounds, and defines the concept of “uncertainty region” which might be of independent interest.
Journal ArticleDOI
Alignment-Based Network Coding for Two-Unicast-Z Networks
TL;DR: A new linear network coding algorithm for two-unicast-Z networks over the directed acyclic graphs that achieves the rate pair (1, 1) whenever it is feasible in the network is described and a new proof of the classical max-flow min-cut theorem is provided.
References
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