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Network Coding for Large Scale Content Distribution
"... We propose a new scheme for content distribution of large files that is based on network coding. With network coding, each node of the distribution network is able to generate and transmit encoded blocks of information. The randomization introduced by the coding process eases the scheduling of bloc ..."
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Cited by 493 (7 self)
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We propose a new scheme for content distribution of large files that is based on network coding. With network coding, each node of the distribution network is able to generate and transmit encoded blocks of information. The randomization introduced by the coding process eases the scheduling of block propagation, and, thus, makes the distribution more efficient. This is particularly important in large unstructured overlay networks, where the nodes need to make decisions based on local information only. We compare network coding to other schemes that transmit unencoded information (i.e. blocks of the original file) and, also, to schemes in which only the source is allowed to generate and transmit encoded packets. We study the performance of network coding in heterogeneous networks with dynamic node arrival and departure patterns, clustered topologies, and when incentive mechanisms to discourage freeriding are in place. We demonstrate through simulations of scenarios of practical interest that the expected file download time improves by more than 2030 % with network coding compared to coding at the server only and, by more than 23 times compared to sending unencoded information. Moreover, we show that network coding improves the robustness of the system and is able to smoothly handle extreme situations where the server and nodes departure the system.
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 316 (29 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.
Coding for errors and erasures in random network coding
, 2007
"... The problem of errorcontrol in random network coding is considered. A “noncoherent” or “channel oblivious ” model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that random network coding is vectorspa ..."
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Cited by 260 (14 self)
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The problem of errorcontrol in random network coding is considered. A “noncoherent” or “channel oblivious ” model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that random network coding is vectorspace preserving, information transmission is modelled as the injection into the network of a basis for a vector space V and the collection by the receiver of a basis for a vector space U. We introduce a metric on the space of all subspaces of a fixed vector space, and show that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space V ∩ U is large enough. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finitefield Grassmannian. Spherepacking and spherecovering bounds as well as generalization of the Singleton bound are provided for such codes. Finally, a ReedSolomonlike code construction, related to Gabidulin’s construction of maximum rankdistance codes, is provided.
On coding for reliable communication over packet networks
, 2008
"... We consider the use of random linear network coding in lossy packet networks. In particular, we consider the following simple strategy: nodes store the packets that they receive and, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of ..."
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Cited by 217 (37 self)
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We consider the use of random linear network coding in lossy packet networks. In particular, we consider the following simple strategy: nodes store the packets that they receive and, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of stored packets. In such a strategy, intermediate nodes perform additional coding yet do not decode nor wait for a block of packets before sending out coded packets. Moreover, all coding and decoding operations have polynomial complexity. We show that, provided packet headers can be used to carry an amount of sideinformation that grows arbitrarily large (but independently of payload size), random linear network coding achieves packetlevel capacity for both single unicast and single multicast connections and for both wireline and wireless networks. This result holds as long as packets received on links arrive according to processes that have average rates. Thus packet losses on links may exhibit correlations in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of random linear network coding shows not only that it achieves packetlevel capacity, but also that the propagation of packets carrying “innovative ” information follows the propagation of jobs through a queueing network, thus implying that fluid flow models yield good approximations.
Information exchange in wireless networks with network coding and physicallayer broadcast,”
 in Proceedings of the 39th Annual Conference on information Sciences and Systems (CISS ’05),
, 2005
"... AbstractWe show that mutual exchange of independent information between two nodes in a wireless network can be efficiently performed by exploiting network coding and the physicallayer broadcast property offered by the wireless medium. The proposed approach improves upon conventional solutions that ..."
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Cited by 196 (5 self)
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AbstractWe show that mutual exchange of independent information between two nodes in a wireless network can be efficiently performed by exploiting network coding and the physicallayer broadcast property offered by the wireless medium. The proposed approach improves upon conventional solutions that separate the processing of the two unicast sessions, corresponding to information transfer along one direction and the opposite direction. 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. INTRODUCTION In this paper, we investigate the mutual exchange of independent information between two nodes in a wireless network. Let us name the two nodes in consideration a and b, respectively. Consider a packetbased communication network with all packets of equal size. The basic problem is very simple: a wants to transmit a sequence of packets {X 1 (n)} to b and b wants to transmit a sequence of packets {X 2 (n)} to a. Assume the two sequences of information packets, {X 1 (n)} and {X 2 (n)}, are from two independent information sources. Information exchange finds many useful applications. These include voice conversations, video conferencing between two participants, and instant messaging. In fact, the scope of information exchange goes much further beyond the generic twoway endtoend communications listed above. Note that a and b do not have to be the true communication endpoints for the packets {X 1 (n)} and {X 2 (n)}. For example, in a wireless ad hoc network where every node can act as a router, information exchange occurs as long as there are some packets {X 1 (n)} to be routed through a to b and some other packets {X 2 (n)} to be routed through b to a. This is illustrated in An information exchange session between a and b is essentially two unicast sessions, one from a to b and the other from b to a. Since the two unicast sessions carry independent information, it may appear that the two sessions can be treated separately, by devoting a first route for packets {X 1 (n)} to flow from a to b and a second route for packets {X 2 (n)} to flow from b to a. In this paper, we show that a joint
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 195 (7 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.
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 164 (28 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.
Insufficiency of linear coding in network information flow
 IEEE TRANSACTIONS ON INFORMATION THEORY (REVISED JANUARY
, 2005
"... It is known that every solvable multicast network has a scalar linear solution over a sufficiently large finitefield alphabet. It is also known that this result does not generalize to arbitrary networks. There are several examples in the literature of solvable networks with no scalar linear solutio ..."
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Cited by 162 (14 self)
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It is known that every solvable multicast network has a scalar linear solution over a sufficiently large finitefield alphabet. It is also known that this result does not generalize to arbitrary networks. There are several examples in the literature of solvable networks with no scalar linear solution over any finite field. However, each example has a linear solution for some vector dimension greater than one. It has been conjectured that every solvable network has a linear solution over some finitefield alphabet and some vector dimension. We provide a counterexample to this conjecture. We also show that if a network has no linear solution over any finite field, then it has no linear solution over any finite commutative ring with identity. Our counterexample network has no linear solution even in the more general algebraic context of modules, which includes as special cases all finite rings and Abelian groups. Furthermore, we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field (exactly 10 % greater), so the network is not even asymptotically linearly solvable. It follows that, even for more general versions of linearity such as convolutional coding, filterbank coding, or linear time sharing, the network has no linear solution.
A rankmetric approach to error control in random network coding
 IEEE Transactions on Information Theory
"... It is shown that the error control problem in random network coding can be reformulated as a generalized decoding problem for rankmetric codes. This result allows many of the tools developed for rankmetric codes to be applied to random network coding. In the generalized decoding problem induced by ..."
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Cited by 159 (11 self)
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It is shown that the error control problem in random network coding can be reformulated as a generalized decoding problem for rankmetric codes. This result allows many of the tools developed for rankmetric codes to be applied to random network coding. In the generalized decoding problem induced by random network coding, the channel may supply partial information about the error in the form of erasures (knowledge of an error location but not its value) and deviations (knowledge of an error value but not its location). For Gabidulin codes, an important family of maximum rank distance codes, an efficient decoding algorithm is proposed that can fully exploit the correction capability of the code; namely, it can correct any pattern of ǫ errors, µ erasures and δ deviations provided 2ǫ+ µ + δ ≤ d − 1, where d is the minimum rank distance of the code. Our approach is based on the coding theory for subspaces introduced by Koetter and Kschischang and can be seen as a practical way to construct codes in that context. I.