Practical Belief Propagation in Wireless Sensor Networks

1. Practical Belief Propagation in Wireless Sensor Networks Bracha Hod Based on a joint work with: Danny Dolev, Tal Anker and Danny Bickson The Hebrew University of Jerusalem

2. Outline • Introduction to Wireless Sensor Networks • Belief Propagation overview • Efficient Belief Propagation framework for Wireless Sensor Networks • Experimental evaluation • Summary Israeli Networking Seminar May 29, 2008

3. Wireless Sensor Networks • Technology is pushed by breakthroughs in MEMS, wireless communication, battery power, etc. • Wireless Sensor Networks (WSNs) • Wireless network consisting of spatially distributed autonomous devices using sensors • The sensors cooperatively monitor physical or environmental conditions Israeli Networking Seminar May 29, 2008

4. WSN Applications

5. WSN Characteristics • Limited power sources and restricted computational capacities • Wireless medium which imposes constraints, such as collisions and errors • Topology changes due to interference, poor link quality, sleep states, death, etc. • Special network dynamic resulting from the self-organization property • Scaling problems because the network has a large number of nodes Israeli Networking Seminar May 29, 2008

6. History • 1994 - DARPA funded research on ‘Low Power Wireless Integrated Microsensor’ • 1998 - WSN technology has been nurtured in its early stages at UC-Berkeley and UCLA • It is estimated that in the US over $100 million in government funding has been invested in university WSN research projects since then • 2003 - Technology Review from MIT, listed WSN on the top, among 10 emerging technologies, that would impact our future • 2008 – About ten years of academic work has been done in this area but still a long way to go Israeli Networking Seminar May 29, 2008

7. Current Status • Research • Many protocols for routing, synchronization, fault tolerant, localization, collaborative information processing, data aggregation, etc. • Development • Dedicated Operating System and Database system, programming languages and test deployments • Standardization • IEEE 802.15.4, Zigbee, 6lowpan • Still a lot to do • Deployment, integration with other networks, security and scalability Israeli Networking Seminar May 29, 2008

8. Inference in WSNs • Data fusion and processing are the core information gathering activities performed in the sensor nodes • Consequently, inference methods become an increasing research interest in the field of WSNs

9. A B C D Graphical Model • In this model, an undirected graph G = (V,E) is a set of nodes V and arcs E, which represent dependencies among random variables • A complex system is viewed as a combination of many simpler pieces connected by probability theory • The idea: instead of calculating 8-sums we can calculate 4-sums and 2-sums Israeli Networking Seminar May 29, 2008

10. Belief Propagation (BP) • BP is an iterative algorithm for computing maximum or marginal posterior probabilities by a local message passing • BP is associated with rapid convergence, accurate results and good performance in asynchronous environment • When performed on trees, BP converges to the correct values in a finite number of iterations Israeli Networking Seminar May 29, 2008

11. The Min-Sum Variation • The goal is to minimize the overall cost in the network, based on the local cost functions and the constraints between the nodes • Each node transmits to its neighbors a message with its local and joint costs. Each neighbor updates its own belief accordingly and transmits the new belief • Gradually the information is propagated through the network until the nodes converge to a common belief Israeli Networking Seminar May 29, 2008

12. Practical Considerations • The unique constraints and requirements in WSN demand changes in traditional algorithms • Several issues to address • Mapping WSN to graphical model • Robustness against failures • Scalability Israeli Networking Seminar May 29, 2008

13. X1 m12 m21 X2 m32 m24 m42 m23 X4 X3 m45 m54 X5 Mapping WSN to Graphical Model • Loopy BP • Operates on a cyclic network • Usually works well because the cycles are large • Junction Tree • Creates a tree based on the cliques in the graph • Scales exponentially with the number of nodes • Involves high overhead Israeli Networking Seminar May 29, 2008

14. Robustness against Failures • Broadcast communication • The message update rule is not an atomic operation which may result in erroneous calculation • Synchronization problems • Asynchronous messages may harm the accuracy • Topology changes • Alink break in the middle of the message-passing may badly affect the convergence Israeli Networking Seminar May 29, 2008

15. Scalability • The original BP algorithm is based on a local message passing, but it is not scalable • The process is performed in the entire network • The convergence depends on the size of the network, and as a result, time and message complexity are not constant Israeli Networking Seminar May 29, 2008

16. Our Solution • Adoption of two WSNs’ approaches • Localized Algorithms • Data-centric • Resulting in Approximation by a set of local optimums instead of a single global optimum  Energy-efficient, fully distributed, asynchronous, robust and scale scheme Israeli Networking Seminar May 29, 2008

17. Efficient BP Framework • Construction of multiple trees according to the routing tree properties and the information that the nodes hold • Every tree is created on-the-fly using a special message, without any maintenance • A “round” field in each message helps in dealing with the asynchronous process • Part of the errors may be detected and overcome • Scalability is achieved by operating in a restricted region, with limited number of rounds Israeli Networking Seminar May 29, 2008

18. Empirical Evaluation • Case study: clustering • The challenge is to efficiently form a connected disjointed group of nodes in a local and distributed manner. Each group contains a single leader and several ordinary nodes Israeli Networking Seminar May 29, 2008

19. Simulation Framework • Simulation in TOSSIM, TinyOS simulator • 5 different time slots were used to validate the behavior on different network topologies • The localized algorithm vicinity was set to 2 with constant number of rounds equal to 8 • In the simulation, the average density is 14 which means that the optimal number of clusters for 50 nodes is about 4 Israeli Networking Seminar May 29, 2008

20. Simulation Results • Network topology • Message-passing trees • Clustered network Israeli Networking Seminar May 29, 2008

21. Simulation Results • Number of clusters per 50 nodes • Percent of nodes who have a cluster head Israeli Networking Seminar May 29, 2008

22. Simulation Results • Percent of nodes who reach a full convergence • Average loss messages in a message-passing tree Israeli Networking Seminar May 29, 2008

23. Summary • WSNs are envisioned to become an integral part of our lives, in applications such as environmental monitoring, smart spaces, medical monitoring, etc. • Two leading approaches: localized algorithms and data-centric, are essential for the design of practical and robust algorithms in WSNs • BP is a promising approach to solve inference tasks in WSNs, when combined with these two approaches. Israeli Networking Seminar May 29, 2008

24. Thank You! Israeli Networking Seminar May 29, 2008