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
On the capacity of information networks
TL;DR: An outer bound on the rate region of noise-free information networks is given and it is shown that multicommodity flow solutions achieve the capacity in an infinite class of undirected graphs, thereby making progress on a conjecture of Li and Li.
Book
Network Coding Applications
TL;DR: This tutorial deals with wireless and content distribution networks, considered to be the most likely applications of network coding, and it also reviews emerging applications ofnetwork coding such as network monitoring and management.
Journal ArticleDOI
Network Coding Theory: A Survey
TL;DR: This article surveys all known fields of network coding theory and leads the reader through the antecedents of the network coding Theory to the most recent results, considering also information theory and matroid theory.
Proceedings ArticleDOI
The Capacity Region for Multi-source Multi-sink Network Coding
TL;DR: By carefully bounding the constrained regions in the entropy space, the exact characterization of the capacity region is obtained, thus closing the existing gap between the above inner and outer bounds.
Journal ArticleDOI
A Constant Bound on Throughput Improvement of Multicast Network Coding in Undirected Networks
TL;DR: It is proved that in undirected networks, the ratio of achievable multicast throughput with network coding to that without network coding is bounded by a constant ratio of 2, i.e., network coding can at most double the throughput.
References
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Book
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Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
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Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
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TL;DR: This work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated, and by employing coding at the nodes, which the work refers to as network coding, bandwidth can in general be saved.
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Flows in networks
D. R. Ford,D. R. Fulkerson +1 more
TL;DR: Ford and Fulkerson as mentioned in this paper set the foundation for the study of network flow problems and developed powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming.