routing in error-correcting networks
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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Routing in Error-Correcting Networks
Edwin Soedarmadji
May 10, 2006
California Institute of TechnologyDepartment of Electrical EngineeringPasadena, CA 91125, USA
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
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
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
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
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
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?
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
Theorem
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
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
= = 12
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
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
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
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.
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
Edge model: Symmetric Channel
U A
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
The Cascaded SC
U A
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
U A
The ary Erasure Channel
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
Generalized Dijkstra Algorithm
x + min( y , z ) = min ( x + y , x + z )
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
The Error Distribution
M U F F L E R M A R B L E S
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
Edge Weight: Worst-Case Error
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 70.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 7
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 70.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 7
p = 0.10 p = 0.25
p = 0.98p = 0.50
May 10, 2006 Maximum Capacity QoS Metric Lee Center Workshop 06
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?