Theory of linear and integer programming
Theory of linear and integer programming
Practical loss-resilient codes
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Integrality ratio for group Steiner trees and directed steiner trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Polynomial time algorithms for network information flow
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Complexity classification of network information flow problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Insufficiency of linear coding in network information flow
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Information flow decomposition for network coding
IEEE Transactions on Information Theory
The encoding complexity of network coding
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Network coding for routability improvement in VLSI
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
Foundations and Trends® in Networking
MACRO+: a network coding driven integrated MAC/routing protocol for multihop wireless networks
Proceedings of the 1st international conference on MOBILe Wireless MiddleWARE, Operating Systems, and Applications
Average throughput with linear network coding over finite fields: the combination network case
EURASIP Journal on Wireless Communications and Networking - Advances in Error Control Coding Techniques
An overview of network coding for dynamically changing networks
International Journal of Autonomous and Adaptive Communications Systems
Toward network coding-based protocols for data broadcasting in wireless ad hoc networks
IEEE Transactions on Wireless Communications
A constant bound on throughput improvement of multicast network coding in undirected networks
IEEE Transactions on Information Theory
Path gain algebraic formulation for the scalar linear network coding problem
IEEE Transactions on Information Theory
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We examine the throughput benefits that network coding offers with respect to the average throughput achievable by routing, where the average throughput refers to the average of the rates that the individual receivers experience. We relate these benefits to the integrality gap of a standard linear programming formulation for the directed Steiner tree problem. We describe families of configurations over which network coding at most doubles the average throughput, and analyze a class of directed graph configurations with N receivers where network coding offers benefits proportional to √N. We also discuss other throughput measures in networks, and show how in certain classes of networks, average throughput bounds can be translated into minimum throughput bounds, by employing vector routing and channel coding. Finally, we show configurations where use of randomized coding may require an alphabet size exponentially larger than the minimum alphabet size required.