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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: 

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

The Gas Station Problem: 

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 

The Gas Station Problem: 

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? 

Theorem: 

Theorem

Example: 

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

Error-Correcting Network: 

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

Error Budget: 

Error Budget  M U R F L E S M A R B L E S 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.  

Edge model: Symmetric Channel: 

Edge model: Symmetric Channel

The Cascaded SC: 

The Cascaded SC

The ary Erasure Channel: 

The ary Erasure Channel

Generalized Dijkstra Algorithm: 

Generalized Dijkstra Algorithm x + min( y , z ) = min ( x + y , x + z )

The Error Distribution: 

The Error Distribution

Edge Weight: Worst-Case Error: 

Edge Weight: Worst-Case Error p = 0.10 p = 0.25 p = 0.98 p = 0.50

Routing in Error-Correcting Networks: 

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? 