Optimization-based linear network coding for general connections of continuous flows

@article{Cui2015OptimizationbasedLN,
  title={Optimization-based linear network coding for general connections of continuous flows},
  author={Ying Cui and Muriel M{\'e}dard and Edmund M. Yeh and Douglas J. Leith and Ken R. Duffy},
  journal={2015 IEEE International Conference on Communications (ICC)},
  year={2015},
  pages={4492-4498}
}
  • Ying Cui, M. Médard, +2 authors K. Duffy
  • Published 22 February 2015
  • Computer Science, Mathematics
  • 2015 IEEE International Conference on Communications (ICC)
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of network codes in terms of the number of flows allowed to be coded together, and are not entirely distributed. In this paper, we consider a new method for constructing linear network codes for general connections of continuous flows to minimize the total cost of… Expand
Optimization-Based Linear Network Coding for General Connections of Continuous Flows
TLDR
This paper considers a new method for constructing linear network codes for general connections of continuous flows to minimize the total cost of the edge use based on mixing and proposes two equivalent alternative formulations with discrete mixing and continuous mixing. Expand
A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem
TLDR
This paper introduces linear network mixing coefficients for code constructions of general connections that generalize random linear network coding (RLNC) for multicast connections and presents a probabilistic distributed algorithm with almost sure convergence in finite time by applying Communication Free Learning (CFL). Expand
A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem
TLDR
This paper introduces linear network mixing coefficients for code constructions of general connections that generalize random linear network coding (RLNC) for multicast connections and presents a probabilistic distributed algorithm with almost sure convergence in finite time by applying Communication Free Learning (CFL). Expand
Reliability evaluation of a multicast over coded packet networks
TLDR
The probability that a multicast rate can be transmitted through a coded packet network under a total transmission cost constraint as the reliability metric is defined and an algorithm based on minimal paths is proposed to calculate the reliability measurement of multicast connections and analyze the complexity of the algorithm. Expand

References

SHOWING 1-10 OF 43 REFERENCES
A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem
TLDR
This paper introduces linear network mixing coefficients for code constructions of general connections that generalize random linear network coding (RLNC) for multicast connections and presents a probabilistic distributed algorithm with almost sure convergence in finite time by applying Communication Free Learning (CFL). Expand
Beyond routing: an algebraic approach to network coding
  • M. Médard, R. Koetter
  • Computer Science
  • Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies
  • 2002
TLDR
A new framework for studying networks and their capacity is presented, based on algebraic methods, and it is shown that, if a multicast connection is achievable under different failure scenarios, a single static code can ensure robustness of the connection under all of those failure scenarios. Expand
An Edge Reduction Lemma for linear network coding and an application to two-unicast networks
  • Weifei Zeng, V. Cadambe, M. Médard
  • Mathematics, Computer Science
  • 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
  • 2012
TLDR
This paper recovers an Edge Reduction Lemma - a fundamental connection between edge deletion and the network transfer matrix in the context of the algebraic framework for linear network coding over Koetter-Medard and derives an achievable rate region for the two-unicast problem that is computable purely from the various min-cuts in the graph. Expand
Network Coding with a Cost Criterion
TLDR
It is shown that, while minimum-cost multicast problems without network coding are very difficult except in the special cases of unicast and broadcast, finding minimum- cost subgraphs for single multicast connections with network coding can be posed as a linear optimization problem. Expand
Optimal reverse carpooling over wireless networks - a distributed optimization approach
TLDR
This work presents a decentralized algorithm to obtain optimal routing schemes in presence of coding opportunities, and shows that the primal sub-problem can be expressed as a shortest path problem on an edge-graph, and the proposed algorithm requires each node to exchange information only with its neighbors. Expand
A Random Linear Network Coding Approach to Multicast
TLDR
This work presents a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks, and shows that this approach can take advantage of redundant network capacity for improved success probability and robustness. Expand
Beyond the Butterfly - A Graph-Theoretic Characterization of the Feasibility of Network Coding with Two Simple Unicast Sessions
TLDR
It is proven that the existence of a network coding scheme is equivalent to finding paths with controlled edge overlaps, and the characterization includes the well-studied butterfly graph as a special case. Expand
Minimum-cost multicast over coded packet networks
TLDR
This work reduces the problem of establishing minimum-cost multicast connections over coded packet networks to a polynomial-time solvable optimization problem, and presents decentralized algorithms for solving it. Expand
Pairwise Intersession Network Coding on Directed Networks
TLDR
A graph-theoretic characterization of pairwise intersession network coding is proven based on paths with controlled edge-overlap, which generalizes the edge-disjoint path characterization of noncoded network communication and includes the well-studied butterfly graph as a special case. Expand
Two-unicast is hard
TLDR
It is shown that linear coding is insufficient to achieve capacity, and non-Shannon inequalities are necessary for characterizing capacity, even for two-unicast networks. Expand
...
1
2
3
4
5
...