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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.
Network Coding for Distributed Storage Systems
, 2008
"... Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peertopeer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, ..."
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Cited by 338 (13 self)
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Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peertopeer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, requires less redundancy than simple replication for the same level of reliability. However, since fragments must be periodically replaced as nodes fail, a key question is how to generate encoded fragments in a distributed way while transferring as little data as possible across the network. For an erasure coded system, a common practice to repair from a node failure is for a new node to download subsets of data stored at a number of surviving nodes, reconstruct a lost coded block using the downloaded data, and store it at the new node. We show that this procedure is suboptimal. We introduce the notion of regenerating codes, which allow a new node to download functions of the stored data from the surviving nodes. We show that regenerating codes can significantly reduce the repair bandwidth. Further, we show that there is a fundamental tradeoff between storage and repair bandwidth which we theoretically characterize using flow arguments on an appropriately constructed graph. By invoking constructive results in network coding, we introduce regenerating codes that can achieve any point in this optimal tradeoff.
Minimumenergy multicast in mobile ad hoc networks using network coding,” submitted to
 Proc. IEEE Information Theory Workshop,
, 2004
"... ..."
Deterministic regenerating codes for distributed storage
 IN ALLERTON CONFERENCE ON CONTROL, COMPUTING, AND COMMUNICATION, (URBANACHAMPAIGN, IL
, 2007
"... It is well known that erasure coding can be used in storage systems to efficiently store data while protecting against failures. Conventionally, the design of erasure codes has focused on the tradeoff between redundancy and reliability; under this criterion, an Maximum Distance Separable (MDS) cod ..."
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Cited by 51 (7 self)
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It is well known that erasure coding can be used in storage systems to efficiently store data while protecting against failures. Conventionally, the design of erasure codes has focused on the tradeoff between redundancy and reliability; under this criterion, an Maximum Distance Separable (MDS) code is optimal. However, practical storage systems call for additional considerations. In particular, the codes must be properly maintained to recover from node failures. Previous work by Dimakis et al. studied the problem of properly maintaining erasure codes to reduce the incurred network bandwidth, established fundamental bounds on the minimum repair bandwidth for maintaining MDS codes, and showed that the repair bandwidth can be reduced further at the cost of higher storage. In this paper we present techniques for constructing codes that achieve the optimal tradeoffs between storage efficiency and repair bandwidth.
Mutualcast: An Efficient Mechanism for Content Distribution in a PeertoPeer (P2P) Network
, 2004
"... In this paper, we propose Mutualcast, a new delivery mechanism for content distribution in peertopeer (P2P) networks. Compared with prior onetomany content distribution approaches, Mutualcast splits the tobedistributed content into many small blocks, so that more resourceful nodes may redistri ..."
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Cited by 48 (13 self)
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In this paper, we propose Mutualcast, a new delivery mechanism for content distribution in peertopeer (P2P) networks. Compared with prior onetomany content distribution approaches, Mutualcast splits the tobedistributed content into many small blocks, so that more resourceful nodes may redistribute more blocks, and less resourceful nodes may redistribute less blocks. Each content block is assigned to a single node for distribution, and the node in charge can be a contentrequesting peer node, a noncontentrequesting peer node, or even the source node. The throughput of the distribution is controlled by redistribution queues between the source and the peer nodes. We show that such a strategy fully utilizes the upload bandwidths of all the peer nodes, thereby maximizing the delivery throughput. Furthermore, Mutualcast is simple and flexible. It can be applied to file/software downloading, media streaming, and erasure coded file distribution in a P2P network.
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
Distributed utility maximization for network coding based multicasting: a shortest path approach
 IEEE J. Selected Areas in Communications
, 2005
"... Abstract — A central issue in practically deploying network coding in a shared network is the adaptive and efficient allocation of network resources. This issue can be formulated as an optimization problem of maximizing the netutility – the difference between a utility derived from the attainable ..."
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Cited by 33 (6 self)
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Abstract — A central issue in practically deploying network coding in a shared network is the adaptive and efficient allocation of network resources. This issue can be formulated as an optimization problem of maximizing the netutility – the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning. We develop a primalsubgradient type distributed algorithm to solve this utility maximization problem. The effectiveness of the algorithm hinges upon two key properties we discovered: (1) the set of subgradients of the multicast capacity is the convex hull of the indicator vectors for the critical cuts, and (2) the complexity of finding such critical cuts can be reduced by exploiting the algebraic properties of linear network coding. The extension to multiple multicast sessions is also carried out. The effectiveness of the proposed algorithm is confirmed by simulations on an
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.
Exact Regenerating Codes for Distributed Storage
, 906
"... Abstract—Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. The bandwidth required to repair the system after a node failure also plays a crucial role in the system performance. In [1] authors have shown that a tradeoff ex ..."
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Cited by 3 (0 self)
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Abstract—Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. The bandwidth required to repair the system after a node failure also plays a crucial role in the system performance. In [1] authors have shown that a tradeoff exists between storage and repair bandwidth. They also have introduced the scheme of regenerating codes which meet this tradeoff. In this paper, a scheme of Exact Regenerating Codes is introduced, which are regenerating codes with an additional property of regenerating back the same node upon failure. For the minimum bandwidth point, which is suitable for applications like distributed mail servers, explicit construction for exact regenerating codes is provided. A subspace approach is provided, using which the necessary and sufficient conditions for a linear code to be an exact regenerating code are derived. This leads to the uniqueness of our construction. For the minimum storage point which suits applications such as storage in peertopeer systems, an explicit construction of regenerating codes for certain suitable parameters is provided. This code supports variable number of nodes and can handle multiple simultaneous node failures. The constructions given for both the points require a low field size and have low complexity. I.