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43
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 109 (27 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.
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 107 (26 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.
Information exchange in wireless networks with network coding and physicallayer broadcast
, 2004
"... Abstract — The exchange of independent information between two nodes in a wireless network can be viewed as two unicast sessions, corresponding to information transfer along one direction and the opposite direction. In this paper we show such information exchange can be efficiently performed by expl ..."
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Cited by 106 (5 self)
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Abstract — The exchange of independent information between two nodes in a wireless network can be viewed as two unicast sessions, corresponding to information transfer along one direction and the opposite direction. In this paper we show such information exchange can be efficiently performed by exploiting network coding and the physicallayer broadcast property offered by the wireless medium, which improves upon conventional solutions that separate the processing of the two unicast sessions. 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.
Minimumenergy multicast in mobile ad hoc networks using network coding
 IEEE Trans. Commun
, 2005
"... Abstract — The minimum energy required to transmit a bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that under a layered model of wireless networks, the minimum energyperbit for multicasting in a mobile ad hoc network c ..."
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Cited by 89 (2 self)
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Abstract — The minimum energy required to transmit a bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that under a layered model of wireless networks, the minimum energyperbit for multicasting in a mobile ad hoc network can be found by a linear program; the minimum energyperbit can be attained by performing network coding. Compared with conventional routing solutions, network coding not only promises a potentially lower energyperbit, but also enables the optimal solution to be found in polynomial time, in sharp contrast with the NPhardness of constructing the minimumenergy multicast tree as the optimal routing solution. We further show that the minimum energy multicast formulation is equivalent to a cost minimization with linear edgebased pricing, where the edge prices are the energyperbits of the corresponding physical broadcast links. This paper also investigates minimum energy multicasting with routing. Due to the linearity of the pricing scheme, the minimum energyperbit for routing is achievable by using a single distribution tree. A characterization of the admissible rate region for routing with a single tree is presented. The minimum energyperbit for multicasting with routing is found by an integer linear program. We show that the relaxation of this integer linear program, studied earlier in the Steiner tree literature, can now be interpreted as the optimization for minimum energy multicasting with network coding. In short, this paper presents a unifying study of minimum energy multicasting with network coding and routing. Index Terms — Network coding, routing, multicast, Steiner tree, wireless ad hoc networks, energy efficiency, mobility.
Capacity of Wireless Erasure Networks
 IEEE Transactions on Information Theory
, 2006
"... Abstract—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 requi ..."
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Cited by 86 (10 self)
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Abstract—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. Index Terms—Wireless erasure networks, multicast problems. I.
Network Coding: The Case of Multiple Unicast Sessions
 in Proceedings of the 42nd Allerton Annual Conference on Communication, Control, and Computing
, 2004
"... In this paper, we investigate the benefit of network coding over routing for multiple independent unicast transmissions. We compare the maximum achievable throughput with network coding and that with routing only. We show that the result depends crucially on the network model. In directed network ..."
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Cited by 55 (6 self)
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In this paper, we investigate the benefit of network coding over routing for multiple independent unicast transmissions. We compare the maximum achievable throughput with network coding and that with routing only. We show that the result depends crucially on the network model. In directed networks, or in undirected networks with integral routing requirement, network coding may outperform routing. In undirected networks with fractional routing, we show that the potential for network coding to increase achievable throughput is equivalent to the potential of network coding to increase bandwidth e#ciency, both of which we conjecture to be nonexistent.
Network coding for efficient wireless unicast
 in IEEE International Zurich Seminar on Communications
, 2006
"... Abstract — We consider the problem of establishing efficient unicast connections over wireless packet networks. We show how network coding, combined with distributed flow optimization, gives a practicable approach that promises to significantly outperform the present approach of endtoend or linkb ..."
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Cited by 39 (7 self)
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Abstract — We consider the problem of establishing efficient unicast connections over wireless packet networks. We show how network coding, combined with distributed flow optimization, gives a practicable approach that promises to significantly outperform the present approach of endtoend or linkbylink retransmission combined with route optimization, where performance may be measured in terms of energy consumption, congestion, or any other cost that increases with the number of transmissions made by each node. We present a specific coding scheme and specific distributed flow optimization techniques that may be used to form the basis of a protocol. I.
Network coding for multiple unicasts: An approach based on linear optimization,” presented at the
 IEEE Int. Symp. Inf. Theory
, 2006
"... Abstract—In this paper we consider the application of network coding to a multiple unicast setup. We present two suboptimal, yet practical code construction techniques. One consists of a linear program and the other of an integer program with fewer variables and constraints. We discuss the performan ..."
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Cited by 38 (5 self)
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Abstract—In this paper we consider the application of network coding to a multiple unicast setup. We present two suboptimal, yet practical code construction techniques. One consists of a linear program and the other of an integer program with fewer variables and constraints. We discuss the performance of the proposed techniques as well as their complexity. I.
Control for intersession network coding
 in Proc. Workshop on Network Coding, Theory & Applications
, 2007
"... Abstract — We propose a dynamic routingschedulingcoding strategy for serving multiple unicast sessions when linear network coding is allowed across sessions. Noting that the set of stabilizable throughput levels in this context is an open problem, we prove that our strategy supports any point in t ..."
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Cited by 31 (3 self)
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Abstract — We propose a dynamic routingschedulingcoding strategy for serving multiple unicast sessions when linear network coding is allowed across sessions. Noting that the set of stabilizable throughput levels in this context is an open problem, we prove that our strategy supports any point in the nontrivial region of achievable rates recently characterized by Traskov et al. [1]. This work also provides a theoretical framework in which the gains of intersession network coding and pure routing can be compared. I.
Efficient Broadcasting using Network Coding
, 2008
"... We consider the problem of broadcasting in an adhoc wireless network, where all nodes of the network are sources that want to transmit information to all other nodes. Our figure of merit is energy efficiency, a critical design parameter for wireless networks since it directly affects battery life an ..."
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Cited by 29 (2 self)
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We consider the problem of broadcasting in an adhoc wireless network, where all nodes of the network are sources that want to transmit information to all other nodes. Our figure of merit is energy efficiency, a critical design parameter for wireless networks since it directly affects battery life and thus network lifetime. We prove that applying ideas from network coding allows to realize significant benefits in terms of energy efficiency for the problem of broadcasting, and propose very simple algorithms that allow to realize these benefits in practice. In particular, our theoretical analysis shows that network coding improves performance by a constant factor in fixed networks. We calculate this factor exactly for some canonical configurations. We then show that in networks where the topology dynamically changes, for example due to mobility, and where operations are restricted to simple distributed algorithms, network coding can offer improvements of a factor of log n, where n is the number of nodes in the network. We use the insights gained from the theoretical analysis to propose lowcomplexity distributed algorithms for realistic wireless adhoc scenarios, discuss a number of practical considerations, and evaluate our algorithms through packet level simulation.