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111
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 386 (14 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
 In Proc. of IEEE INFOCOM
, 2007
"... 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 320 (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. I.
Polynomial time algorithms for multicast network code construction
 IEEE TRANS. ON INFO. THY
, 2005
"... The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediat ..."
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Cited by 269 (28 self)
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The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to reencode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity. We extend these algorithms to integer capacities and to codes that are tolerant to edge failures.
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 184 (38 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.
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 171 (6 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.
Computation over MultipleAccess Channels
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2007
"... The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure ..."
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Cited by 136 (24 self)
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The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure of the channel probability transition matrix and the function are appropriately matched. Even when the channel and function are mismatched, these computation codes often outperform separationbased strategies. Achievable distortions are given for the distributed refinement of the sum of Gaussian sources over a Gaussian multipleaccess channel with a joint sourcechannel lattice code. Finally, computation codes are used to determine the multicast capacity of finite field multipleaccess networks, thus linking them to network coding.
Algebraic gossip: A network coding approach to optimal multiple rumor mongering
 IEEE Transactions on Information Theory
, 2004
"... We study the problem of simultaneously disseminating multiple messages in a large network in a decentralized and distributed manner. We consider a network with n nodes and k (k = O(n)) messages spread throughout the network to start with, but not all nodes have all the messages. Our communication mo ..."
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Cited by 117 (10 self)
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We study the problem of simultaneously disseminating multiple messages in a large network in a decentralized and distributed manner. We consider a network with n nodes and k (k = O(n)) messages spread throughout the network to start with, but not all nodes have all the messages. Our communication model is such that the nodes communicate in discretetime steps, and in every timestep, each node communicates with a random communication partner chosen uniformly from all the nodes (known as the random phone call model). The system is bandwidth limited and in each timestep, only one message can be transmitted. The goal is to disseminate rapidly all the messages among all the nodes. We study the time required for this dissemination to occur with high probability, and also in expectation. We present a protocol based on random linear coding (RLC) that disseminates all the messages among all the nodes in O(n) time, which is order optimal, if we ignore the small overhead associated with each transmission. The overhead does not depend on the size of the messages and is less than 1 % for k = 100 and messages of size 100 KB. We also consider a store and forward mechanism without coding, which is a natural extension of gossipbased dissemination with one message in the network. We show that, such an uncoded scheme can do no better than a sequential approach (instead of doing it simultaneously) of disseminating the messages which takes Θ(n ln(n)) time, since disseminating a single message in a gossip network takes Θ(ln(n)) time. 1
Network Coding for Efficient Communication in Extreme Networks
, 2005
"... Some forms of adhoc networks need to operate in extremely performancechallenged environments where endtoend connectivity is rare. Such environments can be found for example in very sparse mobile networks where nodes ”meet ” only occasionally and are able to exchange information, or in wireless s ..."
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Cited by 115 (3 self)
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Some forms of adhoc networks need to operate in extremely performancechallenged environments where endtoend connectivity is rare. Such environments can be found for example in very sparse mobile networks where nodes ”meet ” only occasionally and are able to exchange information, or in wireless sensor networks where nodes sleep most of the time to conserve energy. Forwarding mechanisms in such networks usually resort to some form of intelligent flooding, as for example in probabilistic routing. We propose a communication algorithm that significantly reduces the overhead of probabilistic routing algorithms, making it a suitable building block for a delaytolerant network architecture. Our forwarding scheme is based on network coding. Nodes do not simply forward packets they overhear but may send out information that is coded over the contents of several packets they received. We show by simulation that this algorithm achieves the reliability and robustness of flooding at a small fraction of the overhead.
MinimumEnergy Multicast in Mobile Ad Hoc Networks Using Network Coding
 IEEE Transactions on Communications
, 2005
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