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Practical Network Coding
, 2003
"... We propose a distributed scheme for practical network coding that obviates the need for centralized knowledge of the graph topology, the encoding functions, and the decoding functions, and furthermore obviates the need for information to be communicated synchronously through the network. The resu ..."
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Cited by 462 (15 self)
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We propose a distributed scheme for practical network coding that obviates the need for centralized knowledge of the graph topology, the encoding functions, and the decoding functions, and furthermore obviates the need for information to be communicated synchronously through the network. The result is a practical system for network coding that is robust to random packet loss and delay as well as robust to any changes in the network topology or capacity due to joins, leaves, node or link failures, congestion, and so on. We simulate such a practical network coding system using the network topologies of several commercial Internet Service Providers, and demonstrate that it can achieve close to the theoretically optimal performance.
Minimumenergy multicast in mobile ad hoc networks using network coding,” submitted to
 Proc. IEEE Information Theory Workshop,
, 2004
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A Comparison of Network Coding and Tree Packing
 IN PROC. 2004 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT 2004
, 2004
"... In this paper, we consider the problem of information multicast, namely transmitting common information from a sender s to a set of receivers T , in a communication network. Conventionally, in a communication network such as the Internet, this is done by distributing information over a multicast dis ..."
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Cited by 38 (3 self)
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In this paper, we consider the problem of information multicast, namely transmitting common information from a sender s to a set of receivers T , in a communication network. Conventionally, in a communication network such as the Internet, this is done by distributing information over a multicast distribution tree. The nodes of such a tree are required only to replicate and forward, i.e., route, information received. Recently, Ahlswede et al. [1] demonstrated that it is in general suboptimal to restrict the network nodes to perform only routing. They show that the multicast capacity, which is defined as the maximum rate that a sender can communicate common information to a set of receivers, is given by the minimum C = min t#T C t of maxflows C t = maxflow(s, t) between the sender and each receiver. Moreover, they showed that while the multicast capacity cannot be achieved in general by routing, it can be achieved by network coding. Network coding refers to a scheme where coding is done at the interior nodes in the network, not only at the sender and receivers. Li, Yeung, and Cai [2] showed that it is su#cient for the encoding functions at the interior nodes to be linear. Koetter and Medard[3] gave an algebraic characterization of linear encoding schemes and proved existence of linear timeinvariant codes achieving the multicast capacity. Jaggi, Sanders, et al. [4][5][6] showed for acyclic networks how to find the encoding and decoding coe#cients in polynomial time. Chou, Wu, and Jain [7][8] proposed a distributed scheme for practical network coding in real packet networks achieving throughput close to capacity with low delay that is robust to random packet loss and delay as well as robust to any changes to network topology or capacity
Network coding for multicasting
, 2006
"... In today’s practical networks, endtoend information delivery is performed by routing. Network coding generalizes routing by allowing a node to generate output data by mixing (i.e., computing certain functions of) its received data. Ahlswede et al. determined the multicast capacity in a network of ..."
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Cited by 14 (2 self)
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In today’s practical networks, endtoend information delivery is performed by routing. Network coding generalizes routing by allowing a node to generate output data by mixing (i.e., computing certain functions of) its received data. Ahlswede et al. determined the multicast capacity in a network of lossless links and showed that achieving the multicast capacity requires in general the use of network coding. This thesis presents the following research contributions to the theory and practice of network coding. Constructive network coding We propose and simulate a practical scheme for implementing network coding. We demonstrate its asymptotic optimality by analyzing the connectivity in a continuoustime trellis that models the packet transmissions. Hybrid routing/coding A fundamental theorem by Edmonds established that if all nodes other than the source are destinations, the multicast capacity can be achieved by routing. We constructively prove a theorem that contains Edmonds ’ theorem and Ahlswede et al.’s theorem as special cases. It shows the multicast capacity can still be achieved even if mixing is allowed only on links entering relay nodes.
Distributed Utility Maximization for Network Coding Based Multicasting: A Shortest Path Approach
"... AbstractOne central issue in practically deploying network coding is the adaptive and economic allocation of network resource. We cast this as an optimization, where the netutility the difference between a utility derived from the attainable multicast throughput and the total cost of resource pr ..."
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AbstractOne central issue in practically deploying network coding is the adaptive and economic allocation of network resource. We cast this as an optimization, where the netutility the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning is maximized. By employing the MAX of flows characterization of the admissible rate region for multicasting, this paper gives a novel reformulation of the optimization problem that has a separable structure. The Lagrangian relaxation method is applied to decompose the problem into subproblems involving one destination each. Our specific formulation of the primal problem results in two key properties. First, the resulting subproblem after decomposition amounts to the problem of finding a shortest path from the source to each destination. Second, assuming the netutility function is strictly concave, our proposed method enables a nearoptimal primal variable to be uniquely recovered from a nearoptimal dual variable. A numerical robustness analysis of the primal recovery method is also conducted. For illconditioned problems that arise, for instance, when the cost functions are linear, we propose to use the proximal method, which solves a sequence of wellconditioned problems obtained from the original problem by adding quadratic regularization terms. Furthermore, the simulation results confirm the numerical robustness of the proposed algorithms. Finally, the proximal method and the dual subgradient method can be naturally extended to provide an effective solution for applications with multiple multicast sessions.
Problems with Network Coding in Overlay Networks
"... Network coding is recently proposed mechanism [6] in which intermediate network nodes are not only limited to routing the data, but can also encode or decode it. Network coding is interesting because if network coding is allowed, multicast can achieve the theoretical throughput upper bound, which is ..."
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Network coding is recently proposed mechanism [6] in which intermediate network nodes are not only limited to routing the data, but can also encode or decode it. Network coding is interesting because if network coding is allowed, multicast can achieve the theoretical throughput upper bound, which is generally not possible without network coding. In this paper, we discuss some problems that arise when network coding is used in overlay networks, and identify some possible solutions. We primarily focus on performance of coding the data, and on throughput benefits in realistic model of overlay networks. I.