Network Error Correction With Unequal Link Capacities

Kim, Sukwon; Ho, Tracey; Effros, Michelle; Avestimehr, A. Salman

doi:10.1109/tit.2010.2095090

Cited by 25 publications

(36 citation statements)

References 23 publications

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“…When the flow on edge e is f e , a symbol in the alphabet {1, · · · , 2 Nf e } can be transmitted in N channel uses, where N is usually assumed to be a very large positive integer [3], [7]. Accordingly, a network error correction flow, henceforth simply : e ∈ In(Tail(e)) for i ∈ {1, · · · , N}; • a decoder that assigns an estimatem to each v t 's received sequences y N e : e ∈ In(v t ) .…”

Section: Problem Formulationmentioning

confidence: 99%

“…That is, for arbitrary E (1) a , E (2) a ∈ A and every source-sink cut E F c , there exists an edge e such that e ∈ E F c and e / ∈ E…”

Section: The Proof Of Lemma 3 Can Be Found In Appendix Cmentioning

confidence: 99%

“…(3) For sets A (1) , A (2) P(E) such that A (1) ⊆ A (2) and rates R (1) , R (2) ≥ 0 such that R (1) ≤ R (2) , F R (1) ,A (1) ⊆ F R (2) ,A (2) .…”

Section: Appendix a Tradeoffmentioning

confidence: 99%

“…The network error correction flow with unequal flow on every link was first considered in [3]. In [3], the adversary can attack arbitrary z links among a network.…”

Section: Introductionmentioning

confidence: 99%

“…In [3], the adversary can attack arbitrary z links among a network. It derived the capacity of the network error correction flow in two-node networks, which provided the tightest upper bound among all bounds that depend only on cuts.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Allocation of Network Error Correction Flow to Combat Byzantine Attacks

Xiao

Zhao

et al. 2015

IEEE Trans. Commun.

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This paper studies the allocation of information flows in noiseless, memoryless communication networks in the presence of omniscient Byzantine adversary. In such networks, adversary may maliciously modify some edge-flows, and legitimate users should resort to network error correction strategies to transmit data reliably. Unlike prior papers, which focused on the capacities of the networks, we consider the expense of resources used by the flow. Hereby, this paper uses an optimization problem to define the concept of minimum cost network error correction flows. We provide a necessary and sufficient condition of feasibility of the allocation problem, and derive a cut-set outer bound on the feasible region. Using this cut-set bound, we can find the minimum cost network error correction flow in some instances. Moreover, we also consider the relationship between incoming edge-flows and outgoing edge-flows of a vertex. As for the directed acyclic graphs, we propose an algorithm to allocate the network error correction flow. This algorithm is with polynomial time complexity, and proves to be optimal when recoding at intermediate nodes is forbidden. Additionally, in order to justify the necessity of recoding at intermediate nodes, we analyze the benefit of intermediate recoding. On the one hand, we construct a series of instances to prove that intermediate recoding can bring enormous benefits in some networks. On the other hand, numerical analysis shows that the benefit is modest in small random graphs.Index Terms-Adversarial errors, Byzantine adversary, network error correction, cut-set bound, resource allocation, minimum cost.Zhiqing Xiao received the B.S. degree from Beijing University of Posts and Telecommunications, China, in 2011, and he is currently pursuing the Ph.D. degree in Department of Electronic Engineering, Tsinghua University. His research interests include network error correction, network informationtheoretic security, and network information theory.Yunzhou Li (M'06) received the Ph.D. degree from Tsinghua University, Beijing, China, in 2004. Currently, he is a Professorship Researcher at Tsinghua University. He mainly focuses on signal processing technologies in wireless and mobile communications, including spatial-time signal processing, channel estimation, multi-user detection, and synchronization algorithms for CDMA/OFDM system. He is also interested in analysis, optimization design and enhancement of cellular system and WLAN.Ming Zhao (M'98) received the B.S. and Ph.D. degrees from the Department of Electronic Engineering, Tsinghua University, Beijing, China, in 1993 and 1998, respectively. In 1998, he joined the faculty of Tsinghua University. He is currently a Professorship Researcher at the School of Information Science and Technology, Tsinghua University. He is experienced in the R&D of wireless and mobile communication, and his interests include modulation, channel coding, channel capacity, resource management, and network protocol. He has published over 100 conference and journal papers. Xibi...

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Section: Problem Formulationmentioning

confidence: 99%

“…That is, for arbitrary E (1) a , E (2) a ∈ A and every source-sink cut E F c , there exists an edge e such that e ∈ E F c and e / ∈ E…”

Section: The Proof Of Lemma 3 Can Be Found In Appendix Cmentioning

confidence: 99%

“…(3) For sets A (1) , A (2) P(E) such that A (1) ⊆ A (2) and rates R (1) , R (2) ≥ 0 such that R (1) ≤ R (2) , F R (1) ,A (1) ⊆ F R (2) ,A (2) .…”

Section: Appendix a Tradeoffmentioning

confidence: 99%

“…The network error correction flow with unequal flow on every link was first considered in [3]. In [3], the adversary can attack arbitrary z links among a network.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Allocation of Network Error Correction Flow to Combat Byzantine Attacks

Xiao

Zhao

et al. 2015

IEEE Trans. Commun.

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Upper bound for unequal zig-zag network with small downstream

Yang

Gao

2014

Wuhan Univ. J. Nat. Sci.

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On error detection of intermediate nodes offour-node network with small downstream links

Yang

Cai

Guo

2015

Wuhan Univ. J. Nat. Sci.

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We investigate the error detection ability of intermediate nodes of zig-zag network with small downstream link. We show that the error detection capability of zig-zag networks in the presence of z malicious edges and 2z-1 limited links from node B to node u. Also, at last we analyze a family of networks, which shows that the upper bound of network is smaller than the bound we expected, indicating that Singleton bound is not the tightest bound in the particular condition of network. According to this result, we design corresponding encode and decode strategy to reach the bound we propose in this paper.

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Network Error Correction With Unequal Link Capacities

Cited by 25 publications

References 23 publications

Allocation of Network Error Correction Flow to Combat Byzantine Attacks

Allocation of Network Error Correction Flow to Combat Byzantine Attacks

Upper bound for unequal zig-zag network with small downstream

On error detection of intermediate nodes offour-node network with small downstream links

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