1. A Distributed Framework for Correlated Data Gathering in Sensor Networks Kevin Yuen, Ben Liang, Baochun Li IEEE Transactions on Vehicular Technology 2008 1

2. Outline Introduction Problem Formulation Localized Slepian-Wolf Coding Distributed Solution: A Price-Based Framework Implementation Issues Performance Evaluation 2

3. Introduction Recent technological advances have enabled the production of low-cost sensors. Usually sensors are densely deployed in sensor networks. (Overlapping sensing ranges) Find a transmission structure to minimize total energy This framework should be compatible e.g. multi-sink, distributed solution, asynchronous network settings, sink mobility, duty schedules 3

4. Problem Formulation 4

5. Use rate distortion theory to analyze the problem Let S be a spatially correlated random Gaussian vector 5

6. Problem Formulation Goal : Minimize transmission energy Constraints Flow Conservation Channel Contention Rate Admissibility 6

7. Problem Formulation The constraints and the correlated data-gathering problem can be modeled as an exponential- constraint linear programming formulation 7

8. Localized Splepian-Wolf Coding 8

9. 9

10. Distributed Solution: A Price-Based Framework 10

11. Lagrangian Dualization(1/2) Goal: allocate the limited capacity of the wireless shared medium Price-based resource allocation Each wireless link is a basic resource unit A price can reflect the relation between the traffic load of the link and its bandwidth capacity Relax the channel contention constraints with Lagrangian dualization 11

12. Lagrangian Dualization(2/2) The weight of each link is equal to the sum of its energy and capacity cost. 12 energy capacity cost

13. Subgradient Algorithm 13

14. Distributed Algorithm(1/2) 14

15. Distributed Algorithm(2/2) The algorithm requires 3 control packets Flow rates of all links within the cluster Prices for all clusters that are inherent to it The identities of other sensor nodes in its neighborhood and their distance to destination sink node 90sensors, 10sinks, Transmission rage=30m 15

16. Asynchronous Network Model 16

17. Implementation Issues Primal Recovery Guarantee to generate feasible primal solution The network must remain static 17

18. Implementation Issues Capacity Reservation The rate allocation generated by subgradient algorithm often violate the channel contention constraints Generate feasible solutions by reserving a suitable amount of capacity (e.g. 10%) Handling Network Dynamics Nodes retrieve up-to-date topology in their neighborhood 18

19. Performance Evaluation 19

20. Simulation Environments 20

21. Converge Speed Chose 10% as sink nodes The algorithm is executed in synchronous environment with 500 iterations 21 Primal Sub gradient

22. Impact of Asynchronous Network Settings Run 500 iterations with different time bounds B = 1,5,10,25 The convergence speed is associated with the time bound B. 22 Primal Sub gradient

23. Effect of Data Correlation Compare the effect of data correlation between synchronous and independent environment. D = 0.001, 0.01 and 0.1 W = 0.9 to 0.9999 23 Implementation I : local Implementation II: global

24. Adaptation to Sink Mobility 24

25. Adaptation to Duty Schedules 25