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53
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 29 (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.
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 18 (5 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
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 7 (1 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.
Recursive code construction for random networks,” 2008, available at http://arxiv.org/abs/0806.3650v1
"... We present a modification of KötterKschischang codes for random networks (these codes were also studied by Wang et al. in the context of authentication problems). The new codes have higher information rate, while maintaining the same errorcorrecting capabilities. An efficient errorcorrecting algo ..."
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Cited by 6 (0 self)
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We present a modification of KötterKschischang codes for random networks (these codes were also studied by Wang et al. in the context of authentication problems). The new codes have higher information rate, while maintaining the same errorcorrecting capabilities. An efficient errorcorrecting algorithm is presented for these codes. 1
On the decoder error probability of bounded rankdistance decoders for maximum rank distance codes
 IEEE Trans. Info. Theory
"... Abstract — In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes that parallel those of maximum distance separable c ..."
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Cited by 6 (5 self)
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Abstract — In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes that parallel those of maximum distance separable codes. Using these properties, we show that, for MRD codes with error correction capability t, the decoder error probability of bounded rank distance decoders decreases exponentially with t 2 based on the assumption that all errors with the same rank are equally likely. Index Terms — Bounded distance decoder, decoder error probability, rank metric codes. I.
On the capacity of noncoherent network coding
 in Proc. IEEE Int. Symp. Inf. Theory, Seoul, Korea
, 2009
"... Dedicated to the memory of our dear friend, Ralf Koetter (1963–2009) Abstract—We consider the problem of multicasting information from a source to a set of receivers over a network where intermediate network nodes perform randomized linear network coding operations on the source packets. We propose ..."
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Cited by 6 (1 self)
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Dedicated to the memory of our dear friend, Ralf Koetter (1963–2009) Abstract—We consider the problem of multicasting information from a source to a set of receivers over a network where intermediate network nodes perform randomized linear network coding operations on the source packets. We propose a channel model for the noncoherent network coding introduced by Koetter and Kschischang in [6], that captures the essence of such a network operation, and calculate the capacity as a function of network parameters. We prove that use of subspace coding is optimal, and show that, in some cases, the capacityachieving distribution uses subspaces of several dimensions, where the employed dimensions depend on the packet length. This model and the results also allow us to give guidelines on when subspace coding is beneficial for the proposed model and by how much, in comparison to a coding vector approach, from a capacity viewpoint. We extend our results to the case of multiple source multicast that creates a virtual multiple access channel. Index Terms—Channel capacity, multisource multicast, network coding, noncoherent communication, randomized network coding, subspace coding. I.
Secure Network Coding for Wireless Mesh Networks: Threats, Challenges, and Directions
"... In recent years, network coding has emerged as a new communication paradigm that can significantly improve the efficiency of network protocols by requiring intermediate nodes to mix packets before forwarding them. Recently, several realworld systems have been proposed to leverage network coding in ..."
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Cited by 6 (3 self)
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In recent years, network coding has emerged as a new communication paradigm that can significantly improve the efficiency of network protocols by requiring intermediate nodes to mix packets before forwarding them. Recently, several realworld systems have been proposed to leverage network coding in wireless networks. Although the theoretical foundations of network coding are well understood, a realworld system needs to solve a plethora of practical aspects before network coding can meet its promised potential. These practical design choices expose network coding systems to a wide range of attacks. We identify two general frameworks (interflow and intraflow) that encompass several network codingbased systems proposed in wireless networks. Our systematic analysis of the components of these frameworks reveals vulnerabilities to a wide range of attacks, which may severely degrade system performance. Then, we identify security goals and design challenges in achieving security for network coding systems. Adequate understanding of both the threats and challenges is essential to effectively design secure practical network coding systems. Our paper should be viewed as a cautionary note pointing out the frailty of current network codingbased wireless systems and a general guideline in the effort of achieving security for network coding systems. Key words: Wireless network coding, network coding attacks, network coding security 1.
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 5 (1 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.
Construction and Covering Properties of ConstantDimension Codes
 IN: PROC. OF THE 2009 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT 2009
, 2009
"... Constantdimension codes (CDCs) have been investigated for noncoherent error correction in random network coding. The maximum cardinality of CDCs with given minimum distance and how to construct optimal CDCs are both open problems, although CDCs obtained by lifting Gabidulin codes, referred to as KK ..."
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Cited by 4 (3 self)
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Constantdimension codes (CDCs) have been investigated for noncoherent error correction in random network coding. The maximum cardinality of CDCs with given minimum distance and how to construct optimal CDCs are both open problems, although CDCs obtained by lifting Gabidulin codes, referred to as KK codes, are nearly optimal. In this paper, we first construct a new class of CDCs based on KK codes, referred to as augmented KK codes, whose cardinalities are greater than previously proposed CDCs. We then propose a lowcomplexity decoding algorithm for our augmented KK codes using that for KK codes. Our decoding algorithm corrects more errors than a bounded subspace distance decoder by taking advantage of the structure of our augmented KK codes. In the rest of the paper we investigate the covering properties of CDCs. We first derive bounds on the minimum cardinality of a CDC with a given covering radius and then determine the asymptotic behavior of this quantity. Moreover, we show that liftings of rank metric codes have the highest possible covering radius, and hence liftings of rank metric codes are not optimal packing CDCs. Finally, we construct good covering CDCs by permuting liftings of rank metric codes.