Unachievability of network coding capacity

Dougherty, Randall; Freiling, Chris; Zeger, K.

doi:10.1109/tit.2006.874405

Cited by 68 publications

(77 citation statements)

References 8 publications

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“…At present, very few exact coding capacities have been rigorously derived in the literature. It is also known that the coding capacity might not be achievable [6].…”

Section: ]) Is Coding Solution In Overmentioning

confidence: 99%

“…In addition to the Vámos network, we demonstrate that some specific known networks can be constructed from matroids. These include the Butterfly network from [2], and parts of networks used to establish the insufficiency of linear network coding in [5] and the unachievability of network coding capacity in [6].…”

Section: ]) Is Coding Solution In Overmentioning

confidence: 99%

“…A set is a cutset for a node in if for every source that generates a message not in , every path 6 from to contains an edge in .…”

Section: Example Iii4mentioning

confidence: 99%

“…Correspondingly, the Fano network was shown in [6], to be solvable if and only if the alphabet size is an integer power of two. It, in fact, has a linear solution over any finite field of characteristic two (by taking , , , and ).…”

Section: The Fano Networkmentioning

confidence: 99%

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Networks, Matroids, and Non-Shannon Information Inequalities

Dougherty

Freiling

Zeger

2007

IEEE Trans. Inform. Theory

215

298

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Abstract-We define a class of networks, called matroidal networks, which includes as special cases all scalar-linearly solvable networks, and in particular solvable multicast networks. We then present a method for constructing matroidal networks from known matroids. We specifically construct networks that play an important role in proving results in the literature, such as the insufficiency of linear network coding and the unachievability of network coding capacity. We also construct a new network, from the Vámos matroid, which we call the Vámos network, and use it to prove that Shannon-type information inequalities are in general not sufficient for computing network coding capacities. To accomplish this, we obtain a capacity upper bound for the Vámos network using a non-Shannon-type information inequality discovered in 1998 by Zhang and Yeung, and then show that it is smaller than any such bound derived from Shannon-type information inequalities. This is the first application of a non-Shannon-type inequality to network coding. We also compute the exact routing capacity and linear coding capacity of the Vámos network. Finally, using a variation of the Vámos network, we prove that Shannon-type information inequalities are insufficient even for computing network coding capacities of multiple-unicast networks.

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“…At present, very few exact coding capacities have been rigorously derived in the literature. It is also known that the coding capacity might not be achievable [6].…”

Section: ]) Is Coding Solution In Overmentioning

confidence: 99%

Section: ]) Is Coding Solution In Overmentioning

confidence: 99%

“…A set is a cutset for a node in if for every source that generates a message not in , every path 6 from to contains an edge in .…”

Section: Example Iii4mentioning

confidence: 99%

Section: The Fano Networkmentioning

confidence: 99%

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Networks, Matroids, and Non-Shannon Information Inequalities

Dougherty

Freiling

Zeger

2007

IEEE Trans. Inform. Theory

215

298

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“…Network examples are provided: for the exponential alphabet size and for the non-monotonicity of alphabet size by Rasala Lehman and Lehman [50]; for nonlinearity by Riis [71] and Dougherty et al [17]; and for non-reversibility by Riis [70] and Dougherty and Zeger [18]. Constructive algorithms to support multiple unicast sessions were proposed for example by Ho et al [33].…”

Section: Notesmentioning

confidence: 99%

Network Coding Applications

Fragouli

Soljanin²

2007

FNT in Networking

135

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Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance. It is expected to be a critical technology for networks of the future. 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 of network coding such as network monitoring and management. Multiple unicasts, security, networks with unreliable links, and quantum networks are also addressed. The preceding companion deals with theoretical foundations of network coding.

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Network coding for efficient network multicast

Soljanin¹,

Gupta²,

Kramer³

2009

Bell Labs Tech. J.

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and consumed do not necessarily need to be kept separate when they are transported throughout the network: there are ways to combine and later extract independent information.Combining independent data streams enables us to better tailor the information flow to the network environment and accommodate the demands of specific traffic patterns. This shift in paradigm is expected to revolutionize the way we manage, operate, and even understand networks and will have a deep impact on a wide range of areas such as reliable delivery, resource sharing, efficient flow control, network monitoring, and security.Network coding is expected to play an important role in the way the coming generations of networks will be designed and operated. Theoretical results obtained since the introduction of network coding show its enormous potential for improving network performance [18,19]. Depending on the traffic scenario, on whether the network is wireless or wired,

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Unachievability of network coding capacity

Cited by 68 publications

References 8 publications

Networks, Matroids, and Non-Shannon Information Inequalities

Networks, Matroids, and Non-Shannon Information Inequalities

Network Coding Applications

Network coding for efficient network multicast

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