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Community Networks
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Network Coding
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Linear network coding
Linear network coding,10.1109/TIT.2002.807285,IEEE Transactions on Information Theory,Shuoyen Robert Li,Raymond W. Yeung,Ning Cai
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Linear network coding
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Citations: 1207
)
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Shuoyen Robert Li
,
Raymond W. Yeung
,
Ning Cai
Consider a communication network in which certain source nodes multicast information to other nodes on the network in the multihop fashion where every node can pass on any of its received data to others. We are interested in how fast each node can receive the complete information, or equivalently, what the
information rate
arriving at each node is. Allowing a node to encode its received data before passing it on, the question involves optimization of the multicast mechanisms at the nodes. Among the simplest coding schemes is linear coding, which regards a block of data as a vector over a certain base field and allows a node to apply a
linear transformation
to a vector before passing it on. We formulate this multicast problem and prove that linear coding suffices to achieve the optimum, which is the maxflow from the source to each receiving node.
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 49, no. 2, pp. 371381, 2003
DOI:
10.1109/TIT.2002.807285
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Citation Context
(897)
...The coding techniques for the deterministic case are inspired by and generalize the random network coding technique of [6] and the linear coding technique of [
7
], [8], [17]...
Amir Salman Avestimehr
,
et al.
Wireless Network Information Flow: A Deterministic Approach
...This mixing (or encoding) of information has been extensively studied over the last decade, e.g., [1], [
2
], [3], [4], [5]...
Michael Langberg
,
et al.
On the Hardness of Approximating the Network Coding Capacity
...costs = M k 2d 2d k+1 . Regenerating codes can be implemented using linear codes [
10
]–[14]...
AnneMarie Kermarrec
,
et al.
Repairing Multiple Failures with Coordinated and Adaptive Regenerating...
...The two later were formally published in [3] and [
4
], respectively...
...This is called a generic FLNC in the original theory of LNC [2], [
4
]...
...Besides the original theory of LNC [2], [
4
], the following alternative proof to Corollary 5 is given in [23]...
ShuoYen Robert Li
,
et al.
Linear Network Coding: Theory and Algorithms
...With NC it is possible to acheive maximum multicast capacity [
2
], [6], which is difficult without network coding...
Mohammed D. Halloush
,
et al.
Network Coding with MultiGeneration Mixing: A Generalized Framework f...
References
(2)
Network multicast flow via linear coding
(
Citations: 13
)
S. Y. R. Li
,
R. W. Yeung
Published in 1998.
A First Course in Information Theory
(
Citations: 194
)
Raymond Yeung
Published in 2002.
Sort by:
Citations
(1207)
Wireless Network Information Flow: A Deterministic Approach
(
Citations: 15
)
Amir Salman Avestimehr
,
Suhas N. Diggavi
,
David N. C. Tse
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 57, no. 4, pp. 18721905, 2011
On the Hardness of Approximating the Network Coding Capacity
(
Citations: 7
)
Michael Langberg
,
Alexander Sprintson
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 57, no. 2, pp. 10081014, 2011
Repairing Multiple Failures with Coordinated and Adaptive Regenerating Codes
(
Citations: 4
)
AnneMarie Kermarrec
,
Gilles Straub
,
Nicolas Le Scouarnec
Conference:
Workshop on Network Coding, Theory and Applications  NetCod
, vol. abs/1102.0, 2011
Linear Network Coding: Theory and Algorithms
(
Citations: 2
)
ShuoYen Robert Li
,
Qifu Tyler Sun
,
Ziyu Shao
Journal:
Proceedings of The IEEE  PIEEE
, vol. 99, no. 3, pp. 372387, 2011
Network Coding with MultiGeneration Mixing: A Generalized Framework for Practical Network Coding
(
Citations: 2
)
Mohammed D. Halloush
,
Hayder Radha
Journal:
IEEE Transactions on Wireless Communications  TWC
, vol. 10, no. 2, pp. 466473, 2011