Bouabdellah KECHAR bkechar2000@yahoo.fr Oran University

1. Bouabdellah KECHAR bkechar2000@yahoo.fr Oran University Faculty of science – Department of Computer Science Algeria Using Polynomial Approximation as Compression and Aggregation Technique in Wireless Sensor Networks June 4, 2007 Workshop on Wireless Sensor Networks Marrakech - Morocco

2. Outlines • Introduction • Objective • Related works • Requirements and constraints • Algorithms of compression • Fixed window based • Variable window based • Local aggregation • Experiments and simulation • Conclusion and future works

3. Introduction (1) • Characteristics of WSN • Important density • Limited processing speed • Limited storage capabilities • Limited power supply (energy) • And limited bandwidth Values referenced here are resources available in MICA2mote Need design and development of new protocols and algorithms at each level of WSN-layers stack (independently or using Cross layer approach) in order to minimize the dissipated power and consequently extend network lifetime

4. Introduction (2) • The reduction of the volume of data to be transmitted in WSN constitutes the most convenient method to reduce energy consumption in a WSN. • This is motivated usually by the fact that processing data consumes much less power than transmitting data. • One way to achieve this goal is : Data Compression and Aggregation

5. Contents • Introduction • Objective • Related works • Requirements and constraints • Algorithms of compression • Fixed window based • Variable window based • Local aggregation • Experiments and simulation • Conclusion and future works

6. Objective (1) Polynomial approximation algorithms and Local aggregation Collected data (fixed or variable window) Polynomial packet IN OUT Sensor Channel Wireless Channel Temperature, relative humidity, wind speed, … (Environmental readings)

7. Objective (2) • Applications concerned ? • Environmental monitoring • Temporal constraint is not required • Nature of analysis is qualitative • Resolution method ? • Approach based on the theorem of Stone-Weierstrass(theory of approximation of functions)  Compression • Protocol based on calculation of correlation coefficients between polynomials  Local aggregation • Validation method ? • Simulation using Matlab tool

8. Contents • Introduction • Objective • Related works • Requirements and constraints • Algorithms of compression • Fixed window based • Variable window based • Local aggregation • Experiments and simulation • Conclusion and future works

9. Related works • LTC (Lightweight Temporal Compression) [Schoellhammer & al 2004] • PREMON (PREdiction-based MONitoring) [Goel & al 2001] • TiNA (Temporal in-Network Aggregation) [Sharaf & al 2003] • CAG (Clustered AGgregation) [SunHee & al 2005] • TREG (TREe based data aGgregation) [Torsha & al 2005]

10. Contents • Introduction • Objective • Related works • Requirements and constraints • Algorithms of compression • Fixed window based • Variable window based • Local aggregation • Experiments and simulation • Conclusion and future works

11. Requirements and Constraints • Temporal coherency in physical phenomenon • Environmental data as temperature, humidity and others, have a common property : continuous variation in time for relatively small temporal windows. The evolution of these properties is roughly linear •  this characteristic of natural phenomena allows designers of applications to adapt the model of data collection. • Interpolation and approximation • Stone-Weierstrass theorem • Application scenario and suppositions • Every sensor have: CPU, RAM, RADIO, protocols • Variation of error tolerated by application

12. Contents • Introduction • Objective • Related works • Requirements and constraints • Algorithms of compression • Fixed window based • Variable window based • Local aggregation • Experiments and simulation • Conclusion and future works

13. Algorithms of compression : Fixed Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients ni: sensor node object VarErr: evaluation of polynomial and calculation of variation Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients ni: sensor node object VarErr: evaluation of polynomial and calculation of variation m: Polynomial degree Sensed and collected data at time tj

14. Algorithms of compression : Fixed Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients ni: sensor node object VarErr: evaluation of polynomial and calculation of variation Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients ni: sensor node object VarErr: evaluation of polynomial and calculation of variation m: Polynomial degree Variation of error

15. Algorithms of compression : Fixed Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients ni: sensor node object VarErr: evaluation of polynomial and calculation of variation m: Polynomial degree Find a new polynomial while condition is true, otherwise save polynomial and transmit it

16. Algorithms of compression : Fixed Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients ni: sensor node object VarErr: evaluation of polynomial and calculation of variation Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients ni: sensor node object VarErr: evaluation of polynomial and calculation of variation m: Polynomial degree Start Approximation using Least-Squares method

17. Algorithms of compression : Variable Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients ni: sensor node object VarErr: evaluation of polynomial and calculation of variation WindowMin: minimal size of time window WindowMax: maximal size of time window OldDegree: Degree of last approximation m: Polynomial degree

18. Algorithms of compression : Variable Window Sensed and collected data of initial window

19. Algorithms of compression : Variable Window Initialization

20. Algorithms of compression : Variable Window Check if the old polynomial is extensible

21. Algorithms of compression : Variable Window A new collected value is added and the old degree is saved

22. Algorithms of compression : Variable Window To limit the algorithm by a number of readings (WindowMax)

23. Contents • Introduction • Objective • Related works • Requirements and constraints • Algorithms of compression • Fixed window based • Variable window based • Local aggregation • Experiments and simulation • Conclusion and future works

24. Local Aggregation • Coefficient of correlation With Packet structure Without compression Packet structure With compression Correlated polynomial  Transmit juste Packet structure With compression

25. Contents • Introduction • Objective • Related works • Requirements and constraints • Algorithms of compression • Fixed window based • Variable window based • Local aggregation • Experiments and simulation • Conclusion and future works

26. Experiments and Simulation (1) • Compression ratio during one period • Algorithm with Fixed Window Experiment: samples of 1000 readings (experimental, Temperature, Humidity and Wind speed)  EnvironmentalReal values If we increase the number of readings, that do not imply automatically a corresponding better rate. Contrary, when the window sizes are reduced, the correlation is very expressive and then the approximation process is better. Compression Quality vs Window Size With Tolerable error variation =0.1

27. Experiments and Simulation (2) • Algorithm with Variable Window Compression ratio fully depends on the tolerable variation of error, which implies the strong connection between the quality of data and the desirable compression ratio. Compression Quality vs Tolerable variation of error This table shows that the majority of the values reconstituted by the evaluation of the polynomials will be in the specified margin Restitution Rate

28. Experiments and Simulation (3) • Comparison of compression rate If we fix the variation of error at 0.1 and we consider an optimal size of the fixed window (80 readings) for the algorithm with fixed window, the algorithm with variable window is more powerful.

29. Contents • Introduction • Objective • Related works • Requirements and constraints • Algorithms of compression • Fixed window based • Variable window based • Local aggregation • Experiments and simulation • Conclusion and future works

30. Conclusion • Data compression is an important technique to reduce communications and hence save energy in WSN. • Our proposed approach (New data compression and aggregation technique for WSN) is a simple idea but it is quite novel and interesting. • The results obtained are encouraged to follow this research direction.

31. Perspectives • What are the computation cost and memory requirement at each sensor node ? • A comparison with other compression techniques in terms of accuracy and cost (like TiNA and LTC). • Additional experimental effort to prove the effectiveness of the approach (Energy calculation). • Extend the approach to Multi-objective WSN (several data types in the same network with cooperation capabilities)

32. Using Polynomial Approximation as Compression and Aggregation Technique in Wireless Sensor Networks Thanks for your attention. Questions & remarks