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56
XORs in the air: practical wireless network coding
 In Proc. ACM SIGCOMM
, 2006
"... This paper proposes COPE, a new architecture for wireless mesh networks. In addition to forwarding packets, routers mix (i.e., code) packets from different sources to increase the information content of each transmission. We show that intelligently mixing packets increases network throughput. Our de ..."
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Cited by 264 (16 self)
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This paper proposes COPE, a new architecture for wireless mesh networks. In addition to forwarding packets, routers mix (i.e., code) packets from different sources to increase the information content of each transmission. We show that intelligently mixing packets increases network throughput. Our design is rooted in the theory of network coding. Prior work on network coding is mainly theoretical and focuses on multicast traffic. This paper aims to bridge theory with practice; it addresses the common case of unicast traffic, dynamic and potentially bursty flows, and practical issues facing the integration of network coding in the current network stack. We evaluate our design on a 20node wireless network, and discuss the results of the first testbed deployment of wireless network coding. The results show that COPE largely increases network throughput. The gains vary from a few percent to several folds depending on the traffic pattern, congestion level, and transport protocol.
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 114 (4 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.
Network Information Flow with Correlated Sources
 IEEE Trans. Inform. Theory
, 2006
"... Consider the following network communication setup, originating in a sensor networking application we refer to as the “sensor reachback ” problem. We have a directed graph G = (V, E), where V = {v0v1...vn} and E ⊆ V × V. If (vi, vj) ∈ E, then node i can send messages to node j over a discrete memor ..."
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Cited by 64 (9 self)
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Consider the following network communication setup, originating in a sensor networking application we refer to as the “sensor reachback ” problem. We have a directed graph G = (V, E), where V = {v0v1...vn} and E ⊆ V × V. If (vi, vj) ∈ E, then node i can send messages to node j over a discrete memoryless channel (Xij, pij(yx), Yij), of capacity Cij. The channels are independent. Each node vi gets to observe a source of information Ui (i = 0...M), with joint distribution p(U0U1...UM). Our goal is to solve an incast problem in G: nodes exchange messages with their neighbors, and after a finite number of communication rounds, one of the M + 1 nodes (v0 by convention) must have received enough information to reproduce the entire field of observations (U0U1...UM), with arbitrarily small probability of error. In this paper, we prove that such perfect reconstruction is possible if and only if H(USUSc) < i∈S,j∈Sc Cij, for all S ⊆ {0...M}, S � = ∅, 0 ∈ S c. Close examination of our achievability proof reveals that in this setup, Shannon information behaves as a classical network flow, identical in nature to the flow of water in pipes. This “information as flow ” view provides an algorithmic interpretation for our results, among which we
On the Capacity of Information Networks
"... An outer bound on the rate region of noisefree information networks is given. This outer bound combines properties of entropy with a strong information inequality derived from the structure of the network. This blend of information theoretic and graph theoretic arguments generates many interestin ..."
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Cited by 56 (7 self)
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An outer bound on the rate region of noisefree information networks is given. This outer bound combines properties of entropy with a strong information inequality derived from the structure of the network. This blend of information theoretic and graph theoretic arguments generates many interesting results. For example, the capacity of directed cycles is characterized. Also, a gap between the sparsity of an undirected graph and its capacity is shown. Extending this result, it is shown that multicommodity flow solutions achieve the capacity in an infinite class of undirected graphs, thereby making progress on a conjecture of Li and Li. This result is in sharp contrast to the situation with directed graphs, where a family of graphs are presented in which the gap between the capacity and the rate achievable using multicommodity flows is linear in the size of the graph.
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.
On achieving optimal throughput with network coding
 in Proc. IEEE Infocom 2005
, 2005
"... Abstrkt With the constraints of network topologies and link capacities, achieving the optimal endtoend throughput in data networks has been known as a fundamental but camputationally hard problem, In this paper, we seek efficient solutions to the problem of achieving optimal throughput in data ne ..."
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Cited by 54 (22 self)
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Abstrkt With the constraints of network topologies and link capacities, achieving the optimal endtoend throughput in data networks has been known as a fundamental but camputationally hard problem, In this paper, we seek efficient solutions to the problem of achieving optimal throughput in data networks, with single or multiple unicast, multicast and broadcast sessions. Although previous approaches lead to solving NPcomplete prohlems, we show the surprising result that, facilitated by the recent advances of network coding, computing the strategies to achieve the optimal endtoend throughput can be performed in polynomial time. This result holds for one or more communication sessions, as well as in the overlay network model, Supported by empirical studies, we present the surprising observation that in most topologies, applying network coding may not improve the achievable optimal throughput; rather, it facilitates the design of significantly more efficient algorithms to achieve such optimality.
Bounds on the Gain of Network Coding and Broadcasting in Wireless Networks
 in INFOCOM
, 2007
"... Gupta and Kumar established that the per node throughput of ad hoc networks with multipair unicast traffic scales with an increasing number of nodes ¤ as ¥§¦¨¤�©�����¦����� � ¤�������¤� © , thus indicating that network performance does not scale well. However, Gupta and Kumar did not consider the p ..."
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Cited by 40 (4 self)
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Gupta and Kumar established that the per node throughput of ad hoc networks with multipair unicast traffic scales with an increasing number of nodes ¤ as ¥§¦¨¤�©�����¦����� � ¤�������¤� © , thus indicating that network performance does not scale well. However, Gupta and Kumar did not consider the possibility of network coding and broadcasting in their model, and recent work has suggested that such techniques have the potential to greatly improve network throughput. Here, for multiple unicast flows in a random topology under the protocol communication model of Gupta and Kumar [1], we show that for arbitrary network coding and broadcasting in a �� � random topology that the throughput scales as ¥§¦¨¤�©�����¦�����¤���¦�¤�©� © where ¤ is the total number of nodes and ��¦¨¤� © is the transmission radius. When is set to ensure connectivity, ¥§¦¨¤�©�����¦��� � � ¤�������¤� © , which is of the same order as the lower bound for the throughput without network coding and broadcasting; in other words, network coding and broadcasting at most provides a constant factor improvement in the throughput. This result is also extended to other dimensional random deployment topologies, where it is shown ¥§¦¨¤�©�����¦�����¤� © that for �� � the ¥§¦¨¤�©����� ¦ � � topology, networks ¥���¦¨¤�©����� ¦ � � �����
Network Routing Capacity
, 2005
"... We define the routing capacity of a network to be the supremum of all possible fractional message throughputs achievable by routing. We prove that the routing capacity of every network is achievable and rational, we present an algorithm for its computation, and we prove that every nonnegative ratio ..."
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Cited by 34 (12 self)
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We define the routing capacity of a network to be the supremum of all possible fractional message throughputs achievable by routing. We prove that the routing capacity of every network is achievable and rational, we present an algorithm for its computation, and we prove that every nonnegative rational number is the routing capacity of some network. We also determine the routing capacity for various example networks. Finally, we discuss the extension of routing capacity to fractional coding solutions and show that the coding capacity of a network is independent of the alphabet used.
Challenges: Towards Truly Scalable Ad Hoc Networks
 MobiCom'07
, 2007
"... The protocols used in ad hoc networks today are based on the assumption that the best way to approach multiple access interference (MAI) is to avoid it. Unfortunately, as the seminal work by Gupta and Kumar has shown, this approach does not scale. Recently, Ahlswede, Ning, Li, and Yeung showed that ..."
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Cited by 25 (18 self)
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The protocols used in ad hoc networks today are based on the assumption that the best way to approach multiple access interference (MAI) is to avoid it. Unfortunately, as the seminal work by Gupta and Kumar has shown, this approach does not scale. Recently, Ahlswede, Ning, Li, and Yeung showed that network coding (NC) can attain the maxflow mincut throughput for multicast applications in directed graphs with pointtopoint links. Motivated by this result, many researchers have attempted to make ad hoc networks scale using NC. However, the work by Liu, Goeckel, and Towsley has shown that NC does not increase the order capacity of wireless ad hoc networks for multipair unicast applications. We demonstrate that protocol architectures that exploit multipacket reception (MPR) do increase the order capacity of random wireless ad hoc networks by a factor Θ(log n) under the protocol model. We also show that MPR provides a better capacity improvement for ad hoc networks than NC when the network experiences a singlesource multicast and multipair unicasts. Based on these results, we introduce design problems for channel access and routing based on MPR, such that nodes communicate with one another on a manytomany basis, rather than onetoone as it is done today, in order to make ad hoc networks truly scalable.
Efficient and Distributed Computation of Maximum Multicast Rates
"... The transmission of information within a data network is constrained by network topology and link capacities. In this paper, we study the fundamental upper bound of information multicast rates with these constraints, given the unique replicable and encodable property of information flows. Based on r ..."
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Cited by 23 (16 self)
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The transmission of information within a data network is constrained by network topology and link capacities. In this paper, we study the fundamental upper bound of information multicast rates with these constraints, given the unique replicable and encodable property of information flows. Based on recent information theory advances in coded multicast rates, we are able to formulate the maximum multicast rate problem as a linear network optimization problem, assuming the general undirected network model. We then proceed to apply Lagrangian relaxation techniques to obtain (1) a necessary and sufficient condition for multicast rate feasibility, and (2) a subgradient solution for computing the maximum rate and the optimal routing strategy to achieve it. The condition we give is a generalization of the wellknown conditions for the unicast and broadcast cases. Our subgradient solution takes advantage of the underlying network flow structure of the problem, and therefore outperforms general linear programming solving techniques. It also admits a natural intuitive interpretation, and is amenable to fully distributed implementations.