Edge-Cut Bounds on Network Coding Rates
Citations
14 citations
Cites background from "Edge-Cut Bounds on Network Coding R..."
...Subsequent studies [22], [23] have shown that the (vertex) cut-set bounds are not tight and improved bounds can be obtained by employing more sophisticated edge-cuts....
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...Studies such as those summarized above [20], [22], [23] do not readily capture the geometric constraints of multihop communication in wireless ad-hoc networks....
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14 citations
Cites background or methods or result from "Edge-Cut Bounds on Network Coding R..."
...Unlike the case when sources are correlated, the problem of characterizing graphical bounds for networks with independent sources has been well investigated [2], [16]–[19], [30]....
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...We will review and compare these bounds, such as cut-set bound [16], network sharing bound [17] and progressive d-separating edge-set bound [19] in Section IV....
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...In Section IV, we compare our new bounds with previously known results: cut-set bound [16], network sharing bound [17], the notion of information dominance [18] and progressive d-separating edge-set bound [19]....
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...4The definition of a functional dependence graph used here is different from that defined in Section III, see [19]....
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...In [19] the authors describe a procedure to determine whether a given set of edges bounds the capacity of the given network....
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14 citations
13 citations
13 citations
Cites background or result from "Edge-Cut Bounds on Network Coding R..."
...For broadcast networks, however, the proposed network coding bounds (dubbed as the PdE bounds) [8], [9] coincide with the standard cutset bounds....
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...It is also worth mentioning that the generalized cut-set bounds proposed in this paper (as well as the PdE bounds [8], [9]) are a special case of the LP bounds by Yeung [2, Ch....
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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], [9]....
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...We mention here that our paper was partly motivated by an earlier work by Kramer and Savari [8] and Kramer et al....
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References
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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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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