### Citations

1965 | Network information flow
- Ahlswede, Cai, et al.
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Citation Context ...ork. I. INTRODUCTION Network coding allows routers in a network to execute possibly complex codes in addition to routing; it has been shown that allowing them to do so can increase communication rate =-=[1]-=-. However, taking advantage of this coding at internal nodes means that the sources and destinations must rely on other nodes—nodes they may not have complete control over—to reliably perform certain ... |

1843 |
Graph Theory
- HARARY
- 1969
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Citation Context ... backwards such that one is guaranteed to pass through each node in Nin(D). Construct an embedding of the graph (V,E) in the plane such that S is on the exterior face. Such an embedding always exists =-=[15]-=-. If we select a set of edges making up an undirected cycle—that is, edges constituting a cycle on the underlying undirected graph—then all nodes in the network not on the cycle are divided into those... |

1561 | The Byzantine generals problem.
- Lamport, Shostak, et al.
- 1995
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Citation Context ...over—to reliably perform certain functions. If these internal nodes do not behave correctly, or, worse, maliciously attempt to subvert the goals of the users—constituting a so-called Byzantine attack =-=[2]-=-, [3]—standard network coding techniques fail. O. Kosut is with the Massachusetts Institute of Technology, Cambridge, MA okosut@mit.edu L. Tong is with Cornell University, Ithaca, NY ltong@ece.cornell... |

260 | Coding for errors and erasures in random network coding
- Kötter, Kschischang
- 2008
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Citation Context ...on, [7] looks at two adversary models slightly different from the omniscient one considered in [4], [5] and in this paper. They show that higher rates can be achieved under these alternate models. In =-=[8]-=-, a more general view of the adversary problem is given, whereby the network itself is abstracted into an arbitrary linear transformation. Network coding under Byzantine attacks that are more general ... |

169 | Resilient network coding in the presence of Byzantine adversaries.
- Jaggi, Langberg, et al.
- 2008
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Citation Context ...attacks on network coding were first studied in [6], which looked at detecting adversaries in a random linear coding environment. The z unit-capacity edge adversary problem was solved in [4], [5]. In =-=[7]-=-, the same problem is studied, providing distributed and low complexity coding algorithms to achieve the same asymptotically optimal rates. In addition, [7] looks at two adversary models slightly diff... |

161 |
The byzantine generals strike again.
- Dolev
- 1981
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Citation Context ...to reliably perform certain functions. If these internal nodes do not behave correctly, or, worse, maliciously attempt to subvert the goals of the users—constituting a so-called Byzantine attack [2], =-=[3]-=-—standard network coding techniques fail. O. Kosut is with the Massachusetts Institute of Technology, Cambridge, MA okosut@mit.edu L. Tong is with Cornell University, Ithaca, NY ltong@ece.cornell.edu ... |

118 | Byzantine modification detection in multicast networks using randomized network coding.
- Ho, Leong, et al.
- 2004
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Citation Context ...ding techniques fail to achieve capacity, so we resort to nonlinear codes, and in particular Polytope Codes, to be described. A. Related Work Byzantine attacks on network coding were first studied in =-=[6]-=-, which looked at detecting adversaries in a random linear coding environment. The z unit-capacity edge adversary problem was solved in [4], [5]. In [7], the same problem is studied, providing distrib... |

92 | Network error correction, part i: Basic concepts and upper bounds.
- Yeung, Cai
- 2006
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Citation Context ...l any z unit-capacity edges in the network, then it has been shown that, for the multicast problem (one source and many destinations), the capacity reduces by 2z compared to the non-Byzantine problem =-=[4]-=-, [5]. To achieve this rate, only linear network coding is needed. Furthermore, if there is just one source and one destination, coding is needed only at the source node; internal nodes need only do r... |

74 | Network error correction, part ii: Lower bounds.
- Cai, Yeung
- 2006
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Citation Context ... z unit-capacity edges in the network, then it has been shown that, for the multicast problem (one source and many destinations), the capacity reduces by 2z compared to the non-Byzantine problem [4], =-=[5]-=-. To achieve this rate, only linear network coding is needed. Furthermore, if there is just one source and one destination, coding is needed only at the source node; internal nodes need only do routin... |

29 | Nonlinear network coding is necessary to combat general byzantine attacks
- Kosut, Tong, et al.
- 2009
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Citation Context ...n, whereby the network itself is abstracted into an arbitrary linear transformation. Network coding under Byzantine attacks that are more general than the simple edge-based model was first studied in =-=[9]-=-, a conference version of this work, and [10]. The latter looked at the problem of edge-based attacks when the edges may have unequal capacities. This problem was 4found to have similar complications ... |

19 | Network error correction with unequal link capacities
- Kim, Ho, et al.
- 2009
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Citation Context ...into an arbitrary linear transformation. Network coding under Byzantine attacks that are more general than the simple edge-based model was first studied in [9], a conference version of this work, and =-=[10]-=-. The latter looked at the problem of edge-based attacks when the edges may have unequal capacities. This problem was 4found to have similar complications to the node-based problem. In particular, bot... |

12 | An algebraic watchdog for wireless network coding - Kim, Medard, et al. - 2009 |

11 | When watchdog meets coding
- Liang, Vaidya
- 2010
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Citation Context ...tination. An alternative strategy known as the watchdog, studied for wireless network coding in [11], is for nodes to police downstream nodes by overhearing their messages to detect modifications. In =-=[12]-=-, a similar approach is taken, and they found that nonlinear operations similar to ours can be helpful, in which comparisons are made to detect errors. B. Main Results Many achievability results in ne... |

9 | New results on network error correction: capacities and upper bounds
- Ki, Ho, et al.
- 2010
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Citation Context ...ter version of the cut-set bound in Appendix A. Unlike the problem without adversaries, we see that there is no canonical notion of a cut-set bound. Some even more elaborate bounds are found in [10], =-=[14]-=-. These papers study the unequal-edge problm, but the bounds can be readily applied to the node problem. It was originally conjectured in [10] that even the best cut-set bound is not tight in general.... |

6 |
Maximum distance q -nary codes,” Information Theory
- Singleton
- 1964
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Citation Context ...ect is for the same reason that, in a classical error correction code, the Hamming distance between codewords must be at least twice the number 7of errors to be corrected; this is the Singleton bound =-=[13]-=-. We now give a cut-set upper bound for node-based adversaries in network coding that makes this explicit. A cut in a network is a subset of nodes A ⊂ V containing the source but not the destination. ... |