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
Citations
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Network Coding and Matroid Theory This paper explores the connection between network coding and matroid theory, a branch of mathematics that generalizes linear algebra and graph theory.
TL;DR: This tutorial paper reviews many con- nections between matroids and network coding theory, with specific emphasis on network solvability, admissible network alphabet sizes, linear coding, and network capacity.
Proceedings ArticleDOI
The encoding complexity of network coding with two simple multicast sessions
Wentu Song,Kai Cai,Rongquan Feng +2 more
TL;DR: It is proved that the number of encoding links required to achieve a network coding solution is upper-bounded by max{2,⌊(√2N-7/4)+1/2⌋}.
Modern Low-Complexity Capacity-Achieving Codes For Network Communication - eScholarship
TL;DR: In this article, the authors considered the problem of designing capacity-achieving network codes realizable by modern signal processing circuits and proposed a vector-space function alignment scheme inspired by the concept of interference alignment for channel communications.
Posted Content
Multicut Lower Bounds via Network Coding
TL;DR: A new technique to certify lower bounds on the multicut size using network coding, which identifies a class of networks on which the rate is equal to the size of the minimum multicut and shows this class is closed under the strong graph product.
Proceedings ArticleDOI
Multicut lower bounds via network coding
TL;DR: In this article, the authors introduced a new technique to certify lower bounds on the multicut size using network coding and showed that the problem is closed under the strong graph product, where the rate is equal to the size of the minimum multicut.
References
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