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159
Symbollevel Network Coding for Wireless Mesh Networks
"... This paper describes MIXIT, a system that improves the throughput of wireless mesh networks. MIXIT exploits a basic property of mesh networks: even when no node receives a packet correctly, any given bit is likely to be received by some node correctly. Instead of insisting on forwarding only correct ..."
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Cited by 74 (2 self)
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This paper describes MIXIT, a system that improves the throughput of wireless mesh networks. MIXIT exploits a basic property of mesh networks: even when no node receives a packet correctly, any given bit is likely to be received by some node correctly. Instead of insisting on forwarding only correct packets, MIXIT routers use physical layer hints to make their best guess about which bits in a corrupted packet are likely to be correct and forward them to the destination. Even though this approach inevitably lets erroneous bits through, we find that it can achieve high throughput without compromising endtoend reliability. The core component of MIXIT is a novel network code that operates on small groups of bits, called symbols. It allows the nodes to opportunistically route groups of bits to their destination with low overhead. MIXIT’s network code also incorporates an endtoend error correction component that the destination uses to correct any errors that might seep through. We have implemented MIXIT on a software radio platform running the Zigbee radio protocol. Our experiments on a 25node indoor testbed show that MIXIT has a throughput gain of 2.8 × over MORE, a stateoftheart opportunistic routing scheme, and about 3.9 × over traditional routing using the ETX metric.
On metrics for error correction in network coding
 IEEE Trans. Inf. Theory
, 2009
"... The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and destination nodes, the error correction capability of an (outer ..."
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Cited by 38 (4 self)
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The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and destination nodes, the error correction capability of an (outer) code is succinctly described by the rank metric; as a consequence, it is shown that universal network error correcting codes achieving the Singleton bound can be easily constructed and efficiently decoded. For noncoherent network coding, where knowledge of the network topology and network code is not assumed, the error correction capability of a (subspace) code is given exactly by a new metric, called the injection metric, which is closely related to, but different than, the subspace metric of Kötter and Kschischang. In particular, in the case of a nonconstantdimension code, the decoder associated with the injection metric is shown to correct more errors then a minimumsubspacedistance decoder. All of these results are based on a general approach to adversarial error correction, which could be useful for other adversarial channels beyond network coding. Index Terms Adversarial channels, error correction, injection distance, network coding, rank distance, subspace codes.
Spread codes and spread decoding in network coding
 Proc. IEEE Intern. Symposium on Inform. Theory
, 2008
"... www.math.uzh.ch/aa Abstract — In this paper we introduce the class of Spread Codes for the use in random network coding. Spread Codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding algorithm of spread codes up to h ..."
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Cited by 35 (11 self)
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www.math.uzh.ch/aa Abstract — In this paper we introduce the class of Spread Codes for the use in random network coding. Spread Codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding algorithm of spread codes up to half the minimum distance. I.
Practical defenses against pollution attacks in intraflow network coding for wireless mesh networks
, 2009
"... Recent studies show that network coding can provide significant benefits to network protocols, such as increased throughput, reduced network congestion, higher reliability, and lower power consumption. The core principle of network coding is that intermediate nodes actively mix input packets to prod ..."
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Cited by 32 (6 self)
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Recent studies show that network coding can provide significant benefits to network protocols, such as increased throughput, reduced network congestion, higher reliability, and lower power consumption. The core principle of network coding is that intermediate nodes actively mix input packets to produce output packets. This mixing subjects network coding systems to a severe security threat, known as a pollution attack, where attacker nodes inject corrupted packets into the network. Corrupted packets propagate in an epidemic manner, depleting network resources and significantly decreasing throughput. Pollution attacks are particularly dangerous in wireless networks, where attackers can easily inject packets or compromise devices due to the increased network vulnerability. In this paper, we address pollution attacks against network coding systems in wireless mesh networks. We demonstrate that previous
Recursive code construction for random networks,” 2008, available at http://arxiv.org/abs/0806.3650v1
"... We present a modification of KöetterKschischang codes for random networks. The new codes have higher information rate, while maintaining the same errorcorrecting capabilities. An efficient errorcorrecting algorithm is presented for these codes. 1 ..."
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Cited by 31 (2 self)
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We present a modification of KöetterKschischang codes for random networks. The new codes have higher information rate, while maintaining the same errorcorrecting capabilities. An efficient errorcorrecting algorithm is presented for these codes. 1
Universal secure network coding via rankmetric codes
 IEEE Trans. Inf. Theory
, 2011
"... The problem of securing a network coding communication system against a wiretapper adversary is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the wiretapper can eavesdrop on µ arbitrarily chosen links. A coding scheme is proposed that ..."
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Cited by 29 (6 self)
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The problem of securing a network coding communication system against a wiretapper adversary is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the wiretapper can eavesdrop on µ arbitrarily chosen links. A coding scheme is proposed that can achieve the maximum possible rate of k = n−µ packets that are informationtheoretically secure from the adversary. The scheme, which is based on rankmetric codes, has the distinctive property of being universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying network code. If the security requirements are relaxed to allow only meaningless information to be leaked to the wiretapper, then the scheme can be extended to achieve the full rate of k = n packets, while still preserving the property of universality. A further scenario is considered where the adversary is allowed not only to eavesdrop but also to inject up to t erroneous packets into the network. In this case, as long as µ + 2t < n, the proposed scheme can be extended to provide universal secure and reliable communication. I.
Constantrank codes and their connection to constantdimension codes
, 2008
"... Constantdimension codes have recently received attention due to their significance to error control in noncoherent random network coding. What the maximal cardinality of any constantdimension code with finite dimension and minimum distance is and how to construct the optimal constantdimension cod ..."
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Cited by 26 (1 self)
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Constantdimension codes have recently received attention due to their significance to error control in noncoherent random network coding. What the maximal cardinality of any constantdimension code with finite dimension and minimum distance is and how to construct the optimal constantdimension code (or codes) that achieves the maximal cardinality both remain open research problems. In this paper, we introduce a new approach to solving these two problems. We first establish a connection between constantrank codes and constantdimension codes. Via this connection, we show that optimal constantdimension codes correspond to optimal constantrank codes over sufficiently large extension fields. As such, the two aforementioned problems are equivalent to determining the maximum cardinality of constantrank codes and to constructing optimal constantrank codes, respectively. To this end, we derive bounds on the maximum cardinality of a constantrank code with a given minimum rank distance, propose explicit constructions of optimal or asymptotically optimal constantrank codes, and establish asymptotic bounds on the maximum rate of a constantrank code.
Securing dynamic distributed storage systems against eavesdropping and adversarial attacks,” in arXiv:1009.2556v2
, 2011
"... Abstract—We address the problem of securing distributed storage systems against adversarial node attacks. An important aspect of these systems is node failures over time, necessitating, thus, a repair mechanism in order to maintain a desired high system reliability. In such dynamic settings, an impo ..."
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Cited by 19 (4 self)
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Abstract—We address the problem of securing distributed storage systems against adversarial node attacks. An important aspect of these systems is node failures over time, necessitating, thus, a repair mechanism in order to maintain a desired high system reliability. In such dynamic settings, an important security problem is to safeguard the system from a malicious adversary who may come at different time instances during the lifetime of the storage system to corrupt the data stored on some nodes. We provide upper bounds on the maximum amount of information that can be stored safely on the system in the presence of the adversary. For an important operating regime, which we call the bandwidthlimited regime, we show that our upper bounds are tight and provide explicit linear code constructions. Moreover, we provide a way to shortlist the malicious nodes and expurgate the system. I.
Secure Network Coding for Wiretap Networks of Type II
, 2009
"... We consider the problem of securing a multicast network against a wiretapper that can intercept the packets on a limited number of arbitrary network edges of its choice. We assume that the network employs the network coding technique to simultaneously deliver the packets available at the source to a ..."
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Cited by 18 (2 self)
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We consider the problem of securing a multicast network against a wiretapper that can intercept the packets on a limited number of arbitrary network edges of its choice. We assume that the network employs the network coding technique to simultaneously deliver the packets available at the source to all the receivers. We show that this problem can be looked at as a network generalization of the wiretap channel of type II introduced in a seminal paper by Ozarow and Wyner. In particular, we show that the transmitted information can be secured by using the OzarowWyner approach of coset coding at the source on top of the existing network code. This way, we quickly and transparently recover some of the results available in the literature on secure network coding for wiretap networks. Moreover, we derive new bounds on the required alphabet size that are independent of the network size and devise an algorithm for the construction of secure network codes. We also look at the dual problem and analyze the amount of information that can be gained by the wiretapper as a function of the number of wiretapped edges.