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On Randomized Network Coding
 In Proceedings of 41st Annual Allerton Conference on Communication, Control, and Computing
, 2003
"... We consider a randomized network coding approach for multicasting from several sources over a network, in which nodes independently and randomly select linear mappings from inputs onto output links over some field. This approach was first described in [3], which gave, for acyclic delayfree netwo ..."
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Cited by 200 (35 self)
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We consider a randomized network coding approach for multicasting from several sources over a network, in which nodes independently and randomly select linear mappings from inputs onto output links over some field. This approach was first described in [3], which gave, for acyclic delayfree networks, a bound on error probability, in terms of the number of receivers and random coding output links, that decreases exponentially with code length. The proof was based on a result in [2] relating algebraic network coding to network flows. In this paper, we generalize these results to networks with cycles and delay. We also show, for any given acyclic network, a tighter bound in terms of the probability of connection feasibility in a related network problem with unreliable links. From this we obtain a success probability bound for randomized network coding in linkredundant networks with unreliable links, in terms of link failure probability and amount of redundancy.
Information exchange in wireless networks with network coding and physicallayer broadcast,”
 in Proceedings of the 39th Annual Conference on information Sciences and Systems (CISS ’05),
, 2005
"... AbstractWe show that mutual exchange of independent information between two nodes in a wireless network can be efficiently performed by exploiting network coding and the physicallayer broadcast property offered by the wireless medium. The proposed approach improves upon conventional solutions that ..."
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Cited by 196 (5 self)
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AbstractWe show that mutual exchange of independent information between two nodes in a wireless network can be efficiently performed by exploiting network coding and the physicallayer broadcast property offered by the wireless medium. The proposed approach improves upon conventional solutions that separate the processing of the two unicast sessions, corresponding to information transfer along one direction and the opposite direction. We propose a distributed scheme that obviates the need for synchronization and is robust to random packet loss and delay, and so on. The scheme is simple and incurs minor overhead. I. INTRODUCTION In this paper, we investigate the mutual exchange of independent information between two nodes in a wireless network. Let us name the two nodes in consideration a and b, respectively. Consider a packetbased communication network with all packets of equal size. The basic problem is very simple: a wants to transmit a sequence of packets {X 1 (n)} to b and b wants to transmit a sequence of packets {X 2 (n)} to a. Assume the two sequences of information packets, {X 1 (n)} and {X 2 (n)}, are from two independent information sources. Information exchange finds many useful applications. These include voice conversations, video conferencing between two participants, and instant messaging. In fact, the scope of information exchange goes much further beyond the generic twoway endtoend communications listed above. Note that a and b do not have to be the true communication endpoints for the packets {X 1 (n)} and {X 2 (n)}. For example, in a wireless ad hoc network where every node can act as a router, information exchange occurs as long as there are some packets {X 1 (n)} to be routed through a to b and some other packets {X 2 (n)} to be routed through b to a. This is illustrated in An information exchange session between a and b is essentially two unicast sessions, one from a to b and the other from b to a. Since the two unicast sessions carry independent information, it may appear that the two sessions can be treated separately, by devoting a first route for packets {X 1 (n)} to flow from a to b and a second route for packets {X 2 (n)} to flow from b to a. In this paper, we show that a joint
Network coding: An instant primer
 ACM SIGCOMM Computer Communication Review
, 2006
"... Network coding is a new research area that may have interesting applications in practical networking systems. With network coding, intermediate nodes may send out packets that are linear combinations of previously received information. There are two main benefits of this approach: potential throughp ..."
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Cited by 195 (7 self)
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Network coding is a new research area that may have interesting applications in practical networking systems. With network coding, intermediate nodes may send out packets that are linear combinations of previously received information. There are two main benefits of this approach: potential throughput improvements and a high degree of robustness. Robustness translates into loss resilience and facilitates the design of simple distributed algorithms that perform well, even if decisions are based only on partial information. This paper is an instant primer on network coding: we explain what network coding does and how it does it. We also discuss the implications of theoretical results on network coding for realistic settings and show how network coding can be used in practice.
Hot topic: physicallayer network coding
 in Proc. of ACM Mobicom
, 2006
"... A main distinguishing feature of a wireless network compared with a wired network is its broadcast nature, in which the signal transmitted by a node may reach several other nodes, and a node may receive signals from several other nodes simultaneously. Rather than a blessing, this feature is treated ..."
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Cited by 190 (18 self)
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A main distinguishing feature of a wireless network compared with a wired network is its broadcast nature, in which the signal transmitted by a node may reach several other nodes, and a node may receive signals from several other nodes simultaneously. Rather than a blessing, this feature is treated more as an interferenceinducing nuisance in most wireless networks today (e.g., IEEE 802.11). The goal of this paper is to show how the concept of network coding can be applied at the physical layer to turn the broadcast property into a capacityboosting advantage in wireless ad hoc networks. Specifically, we propose a physicallayer network coding (PNC) scheme to coordinate transmissions among nodes. In contrast to “straightforward ” network coding which performs coding arithmetic on digital bit streams after they have been received, PNC makes use of the additive nature of simultaneously arriving electromagnetic (EM) waves for equivalent coding operation. PNC can yield higher capacity than straightforward network coding when applied to wireless networks. We believe this is a first paper that ventures into EMwavebased network coding at the physical layer and demonstrates its potential for boosting network capacity. PNC opens up a whole new research area because of its implications and new design requirements for the physical, MAC, and network layers of ad hoc wireless stations. The resolution of the many outstanding but interesting issues in PNC may lead to a revolutionary new paradigm for wireless ad hoc networking.
Analyzing and Improving a BitTorrent Network’s Performance Mechanisms
, 2006
"... Abstract — In recent years, BitTorrent has emerged as a very scalable peertopeer file distribution mechanism. While early measurement and analytical studies have verified BitTorrent’s performance, they have also raised questions about various metrics (upload utilization, fairness, etc.), particula ..."
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Cited by 177 (0 self)
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Abstract — In recent years, BitTorrent has emerged as a very scalable peertopeer file distribution mechanism. While early measurement and analytical studies have verified BitTorrent’s performance, they have also raised questions about various metrics (upload utilization, fairness, etc.), particularly in settings other than those measured. In this paper, we present a simulationbased study of BitTorrent. Our goal is to deconstruct the system and evaluate the impact of its core mechanisms, both individually and in combination, on overall system performance under a variety of workloads. Our evaluation focuses on several important metrics, including peer link utilization, file download time, and fairness amongst peers in terms of volume of content served. Our results confirm that BitTorrent performs nearoptimally in terms of uplink bandwidth utilization, and download time except under certain extreme conditions. We also show that low bandwidth peers can download more than they upload to the network when high bandwidth peers are present. We find that the ratebased titfortat policy is not effective in preventing unfairness. We show how simple changes to the tracker and a stricter, blockbased titfortat policy, greatly improves fairness. I.
Resilient Network Coding in the Presence of Byzantine Adversaries
"... Network coding substantially increases network throughput. But since it involves mixing of information inside the network, a single corrupted packet generated by a malicious node can end up contaminating all the information reaching a destination, preventing decoding. This paper introduces distribu ..."
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Cited by 169 (32 self)
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Network coding substantially increases network throughput. But since it involves mixing of information inside the network, a single corrupted packet generated by a malicious node can end up contaminating all the information reaching a destination, preventing decoding. This paper introduces distributed polynomialtime rateoptimal network codes that work in the presence of Byzantine nodes. We present algorithms that target adversaries with different attacking capabilities. When the adversary can eavesdrop on all links and jam zO links, our first algorithm achieves a rate of C − 2zO, where C is the network capacity. In contrast, when the adversary has limited eavesdropping capabilities, we provide algorithms that achieve the higher rate of C − zO. Our algorithms attain the optimal rate given the strength of the adversary. They are informationtheoretically secure. They operate in a distributed manner, assume no knowledge of the topology, and can be designed and implemented in polynomialtime. Furthermore, only the source and destination need to be modified; nonmalicious nodes inside the network are oblivious to the presence of adversaries and implement a classical distributed network code. Finally, our algorithms work over wired and wireless networks.
MinimumCost Multicast over Coded Packet Networks
 IEEE TRANS. ON INF. THE
, 2006
"... We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as b ..."
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Cited by 164 (28 self)
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We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomialtime solvable optimization problem, ... and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimumcost multicast. By contrast, establishing minimumcost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.
Insufficiency of linear coding in network information flow
 IEEE TRANSACTIONS ON INFORMATION THEORY (REVISED JANUARY
, 2005
"... It is known that every solvable multicast network has a scalar linear solution over a sufficiently large finitefield alphabet. It is also known that this result does not generalize to arbitrary networks. There are several examples in the literature of solvable networks with no scalar linear solutio ..."
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Cited by 162 (14 self)
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It is known that every solvable multicast network has a scalar linear solution over a sufficiently large finitefield alphabet. It is also known that this result does not generalize to arbitrary networks. There are several examples in the literature of solvable networks with no scalar linear solution over any finite field. However, each example has a linear solution for some vector dimension greater than one. It has been conjectured that every solvable network has a linear solution over some finitefield alphabet and some vector dimension. We provide a counterexample to this conjecture. We also show that if a network has no linear solution over any finite field, then it has no linear solution over any finite commutative ring with identity. Our counterexample network has no linear solution even in the more general algebraic context of modules, which includes as special cases all finite rings and Abelian groups. Furthermore, we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field (exactly 10 % greater), so the network is not even asymptotically linearly solvable. It follows that, even for more general versions of linearity such as convolutional coding, filterbank coding, or linear time sharing, the network has no linear solution.
Computeandforward: Harnessing interference through structured codes
 IEEE TRANS. INF. THEORY
, 2009
"... ..."
Capacity of Wireless Erasure Networks
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... In this paper, a special class of wireless networks, called wireless erasure networks, is considered. In these networks, each node is connected to a set of nodes by possibly correlated erasure channels. The network model incorporates the broadcast nature of the wireless environment by requiring eac ..."
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Cited by 149 (12 self)
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In this paper, a special class of wireless networks, called wireless erasure networks, is considered. In these networks, each node is connected to a set of nodes by possibly correlated erasure channels. The network model incorporates the broadcast nature of the wireless environment by requiring each node to send the same signal on all outgoing channels. However, we assume there is no interference in reception. Such models are therefore appropriate for wireless networks where all information transmission is packetized and where some mechanism for interference avoidance is already built in. This paper looks at multicast problems over these networks. The capacity under the assumption that erasure locations on all the links of the network are provided to the destinations is obtained. It turns out that the capacity region has a nice maxflow mincut interpretation. The definition of cutcapacity in these networks incorporates the broadcast property of the wireless medium. It is further shown that linear coding at nodes in the network suffices to achieve the capacity region. Finally, the performance of different coding schemes in these networks when no side information is available to the destinations is analyzed.