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Routing in Error-Correcting Networks

Routing in Error-Correcting Networks. Edwin Soedarmadji May 10, 2006 California Institute of Technology Department of Electrical Engineering Pasadena, CA 91125, USA. Introduction. Start from an unrelated network problem Route planning under fuel capacity and refueling constraints

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Routing in Error-Correcting Networks

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  1. Routing in Error-Correcting Networks Edwin Soedarmadji May 10, 2006 California Institute of Technology Department of Electrical Engineering Pasadena, CA 91125, USA

  2. Introduction Start from an unrelated network problem • Route planning under fuel capacity and refueling constraints Especially relevant • Increasing energy cost • Vehicles with alternative fuel • Vehicles exploring remote areas Maximum Capacity QoS Metric

  3. The Gas Station Problem • Shortest Path Problem in • Vehicle has limited a fuel capacity • Refueling nodes in the network • Edge weights expressed in fuel units • Vehicle starts at with fuel units  Maximum Capacity QoS Metric

  4. The Gas Station Problem • Feasible paths are paths where the vehicle always carries a non-negative amount of fuel on the path nodes • Is {all feasible paths} an empty set ? • If not, what is the path that minimizes the travel distance?  Maximum Capacity QoS Metric

  5. Theorem Maximum Capacity QoS Metric

  6. = = 12 Example • Remove infeasible edges in E and vertices in V • Compute all-pairs shortest path between nodes in V’ • Remove infeasible edges in E’ and vertices in V’ • Calculate the shortest path from s to t • Solution produced in Maximum Capacity QoS Metric

  7. Error-Correcting Network Possible Generalization to Communication Networks • The Gas-Station algorithm works for transportation networks • Is it applicable to communication networks? There are many similarities • Vehicle  information packet • Gas tank capacity  error budget • Gas station  error correction node • Gas consumption  packet error Maximum Capacity QoS Metric

  8. Error Budget • Suppose each packet contains seven symbols, and the error-correction scheme employed in the network can correct up to (but not more than) three errors. Then the error budget is three units for a given alphabet size.  M U R F L E S   M A R B L E S Maximum Capacity QoS Metric

  9. U A Edge model: Symmetric Channel Maximum Capacity QoS Metric

  10. U A The Cascaded SC Maximum Capacity QoS Metric

  11. U A The ary Erasure Channel Maximum Capacity QoS Metric

  12. Generalized Dijkstra Algorithm x + min( y , z ) = min ( x + y , x + z ) Maximum Capacity QoS Metric

  13. M U F F L E R M A R B L E S The Error Distribution Maximum Capacity QoS Metric

  14. Edge Weight: Worst-Case Error p = 0.25 p = 0.10 p = 0.50 p = 0.98 Maximum Capacity QoS Metric

  15. Routing in Error-Correcting Networks • WCE x is a non-decreasing function of p • The algorithm used in the Gas Station Problem can be used to find the feasible path with minimum WCE from s to t. • Questions?  Maximum Capacity QoS Metric

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