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
Capacity of Multiple Unicast in Wireless Networks: A Polymatroidal Approach
Sreeram Kannan,Pramod Viswanath +1 more
TL;DR: In this article, the authors show that for a given channel and its reciprocal channel, the min cut upper bound is within a logarithmic factor of the number of sources of the max flow.
Journal ArticleDOI
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, which results in bounds that are tighter than the corresponding cut-set bounds.
Proceedings ArticleDOI
A Multimessage Capacity Region for Undirected Ring Networks
TL;DR: An extension of the Japanese theorem to multiple multicast sessions is developed and it is demonstrated that routing is rate-optimal using new extensions to progressive d-separating edge set bounds.
Proceedings ArticleDOI
Coding in Undirected Graphs Is Either Very Helpful or Not Helpful at All
TL;DR: It is proved that any undirected network with $k$ source-sink pairs that exhibits a $(1+\varepsilon)$ gap between its MCF rate and its network coding rate can be used to construct a family of graphs whose gap is $\log(|G'|)^c$ for some constant $c < 1$.
Book ChapterDOI
Principles of Cognitive Radio: Capacity of cognitive radio networks
TL;DR: In this article, the fundamental capacity limits and associated transmission techniques for different cognitive radio network paradigms are developed based on the premise that the cognitive radios of secondary users are intelligent wireless communication devices that exploit side information about their environment to improve spectrum utilization.
References
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