Edge-Cut Bounds on Network Coding Rates
Citations
7 citations
Cites background from "Edge-Cut Bounds on Network Coding R..."
...The works of [3], [9], [12] provide algorithms to check if their approach can deduce the fundamentality of a given edge-cut....
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...Connection of the GNS bound to the PdE bound [9] and the information dominance bound [3] will be explored in a future work....
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...they can potentially be beaten by network coding [9]....
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...• PdE bound [9] • Information Dominance bound [3] • Functional Dependence bound [12]...
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...[9], [12] study bounds derived from functional dependence graphs and [3] studies bounds derived from information dominance....
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7 citations
7 citations
7 citations
Cites background from "Edge-Cut Bounds on Network Coding R..."
...We mention here that our paper was partly motivated by an earlier work by Kramer and Savari [8], where the idea of combining the properties of Shannon entropy and the graph-theoretic notion of cut to obtain explicit network coding bounds was first explored....
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...For broadcast networks, however, the proposed network coding bounds (dubbed as the PdE bounds) [8] coincide with the standard cut-set bounds....
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...For non-broadcast networks, the union of several simple cuts may not give rise to a super cut that separates the collection of the source nodes from the collection of the sink nodes and hence may not lead to any network coding bounds [8]....
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7 citations
References
45,034 citations
Additional excerpts
...7, we choose Ed = {(2, 3), (4, 3), (2, 5), (4, 5)}, Sd = {1, 2, 3}, [π(1), π(2), π(3)] = [3, 1, 2] and the resulting graph GEd is shown in Fig....
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...7 we choose Ed = {(3, 2), (3, 4), (5, 2), (5, 4)}, Sd = {2, 3}, [π(1), π(2)] = [2, 3]....
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15,671 citations
8,533 citations
"Edge-Cut Bounds on Network Coding R..." refers background in this paper
...For example, it is known that linear network coding is optimal for multicasting a single source in directed networks [1], [9]....
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...The terminals can further perform network coding [1], [9], i....
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...7, we choose Ed = {(2, 3), (4, 3), (2, 5), (4, 5)}, Sd = {1, 2, 3}, [π(1), π(2), π(3)] = [3, 1, 2] and the resulting graph GEd is shown in Fig....
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...Network coding has been intensely studied since [1] presented a novel coding scheme that attains a cut-set bound for multicasting in networks....
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4,341 citations
2,825 citations