Results 1  10
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241
On coding for reliable communication over packet networks
 in Proc. 42nd Annual Allerton Conference on Communication, Control, and Computing, Sept.–Oct. 2004, invited
"... Abstract — We present a capacityachieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission ..."
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Cited by 127 (35 self)
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Abstract — We present a capacityachieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacityachieving as long as packets received on a link arrive according to a process that has an average rate. Thus, packet losses on a link may exhibit correlation 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 the scheme shows that it is not only capacityachieving, but that the propagation of packets carrying “innovative ” information follows the propagation of jobs through a queueing network, and therefore fluid flow models yield good approximations. We consider networks with both lossy pointtopoint and broadcast links, allowing us to model both wireline and wireless packet networks. I.
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 110 (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.
Coding for errors and erasures in random network coding
 in Proc. IEEE Int. Symp. Information Theory
, 2007
"... Abstract — The problem of errorcontrol in a “noncoherent” random network coding channel is considered. 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. A suitable coding metric ..."
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Cited by 97 (12 self)
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Abstract — The problem of errorcontrol in a “noncoherent” random network coding channel is considered. 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. A suitable coding metric on subspaces is defined, under which a minimum distance decoder achieves correct decoding if the dimension of the space V ∩ U is large enough. When the dimension of each codeword is restricted to a fixed integer, the code forms a subset of the vertices of the Grassmann graph. Spherepacking, spherecovering bounds and a Singleton bound are provided for such codes. A ReedSolomonlike code construction is provided and a decoding algorithm given. I.
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 83 (9 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.
Byzantine Modification Detection in Multicast Networks using Randomized Network Coding
 in IEEE Proc. Intl. Sym. Inform. Theory
, 2004
"... We show how distributed randomized network coding, a robust approach to multicasting in distributed network settings, can be extended to provide Byzantine modification detection without the use of cryptographic functions. ..."
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Cited by 82 (12 self)
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We show how distributed randomized network coding, a robust approach to multicasting in distributed network settings, can be extended to provide Byzantine modification detection without the use of cryptographic functions.
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 70 (20 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.
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 55 (7 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.
Dynamic algorithms for multicast with intrasession network coding
 In Proc. 43rd Annual Allerton Conference on Communication, Control, and Computing
, 2005
"... We establish, for multiple multicast sessions with intrasession network coding, the capacity region of input rates for which the network remains stable in ergodically timevarying networks. Building on the backpressure approach introduced by Tassiulas et al., we present dynamic algorithms for mult ..."
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Cited by 50 (13 self)
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We establish, for multiple multicast sessions with intrasession network coding, the capacity region of input rates for which the network remains stable in ergodically timevarying networks. Building on the backpressure approach introduced by Tassiulas et al., we present dynamic algorithms for multicast routing, network coding, rate control, power allocation, and scheduling that achieves stability for rates within the capacity region. Decisions on routing, network coding, and scheduling between different sessions at a node are made locally at each node based on virtual queues for different sinks. For correlated sources, the sinks locally determine and control transmission rates across the sources. The proposed approach yields a completely distributed algorithm for wired networks. In the wireless case, scheduling and power control among different transmitters are centralized while routing, network coding, and scheduling between different sessions at a given node are distributed. 1
Signing a Linear Subspace: Signature Schemes for Network Coding
"... Abstract. Network coding offers increased throughput and improved robustness to random faults in completely decentralized networks. In contrast to traditional routing schemes, however, network coding requires intermediate nodes to modify data packets en route; for this reason, standard signature sch ..."
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Cited by 38 (8 self)
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Abstract. Network coding offers increased throughput and improved robustness to random faults in completely decentralized networks. In contrast to traditional routing schemes, however, network coding requires intermediate nodes to modify data packets en route; for this reason, standard signature schemes are inapplicable and it is a challenge to provide resilience to tampering by malicious nodes. Here, we propose two signature schemes that can be used in conjunction with network coding to prevent malicious modification of data. In particular, our schemes can be viewed as signing linear subspaces in the sense that a signature σ on V authenticates exactly those vectors in V. Our first scheme is homomorphic and has better performance, with both public key size and perpacket overhead being constant. Our second scheme does not rely on random oracles and uses weaker assumptions. We also prove a lower bound on the length of signatures for linear subspaces showing that both of our schemes are essentially optimal in this regard. 1
Network coding for multiple unicasts: An approach based on linear optimization,” presented at the
 IEEE Int. Symp. Inf. Theory
, 2006
"... Abstract—In this paper we consider the application of network coding to a multiple unicast setup. We present two suboptimal, yet practical code construction techniques. One consists of a linear program and the other of an integer program with fewer variables and constraints. We discuss the performan ..."
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Cited by 37 (5 self)
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Abstract—In this paper we consider the application of network coding to a multiple unicast setup. We present two suboptimal, yet practical code construction techniques. One consists of a linear program and the other of an integer program with fewer variables and constraints. We discuss the performance of the proposed techniques as well as their complexity. I.