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

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 Introduction (1) Characteristics of WSN Important density Limited processing speed Limited storage capabilities Limited power supply (energy) And limited bandwidth 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 Values referenced here are resources available in MICA2mote

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 Objective (1) Sensor stack Sensor Layer Physical Layer Sensor Channel Network stack Compression & aggregation Transport Layer Multihop Routing Protocol WSN-MAC Layer Transceiver Unit Wireless Channel Temperature, relative humidity, wind speed, … (Environmental readings) Collected data Polynomial approximation algorithms and Local aggregation Polynomial packet (fixed or variable window) INOUT

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 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]

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Fixed Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients n i : sensor node object VarErr: evaluation of polynomial and calculation of variation Sensed and collected data at time t j Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients n i : sensor node object VarErr: evaluation of polynomial and calculation of variation m: Polynomial degree

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Fixed Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients n i : sensor node object VarErr: evaluation of polynomial and calculation of variation Variation of error Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients n i : sensor node object VarErr: evaluation of polynomial and calculation of variation m: Polynomial degree

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Fixed Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients n i : 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

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Fixed Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients n i : sensor node object VarErr: evaluation of polynomial and calculation of variation Start Approximation using Least-Squares method Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients n i : sensor node object VarErr: evaluation of polynomial and calculation of variation m: Polynomial degree

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Variable Window Dim: number of readings by sequence Tab: collected readings Poly: polynomial coefficients n i : 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

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Variable Window Sensed and collected data of initial window

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Variable Window Initialization

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Variable Window Check if the old polynomial is extensible

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Variable Window A new collected value is added and the old degree is saved

B.KECHAR WWSN – Marrakech – June 4, /32 Algorithms of compression : Variable Window To limit the algorithm by a number of readings (WindowMax)

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 Local Aggregation Coefficient of correlation With IDStntn V1V1 …..VnVn Packet structure Without compression IDStntn P(t i ) Packet structure With compression Correlated polynomial  Transmit juste IDStntn Packet structure With compression

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 Experiments and Simulation (1) Compression ratio during one period Algorithm with Fixed Window Compression Quality vs Window Size With Tolerable error variation =0.1 Experiment: samples of 1000 readings (experimental, Temperature, Humidity and Wind speed)  Environmental Real 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.

B.KECHAR WWSN – Marrakech – June 4, /32 Experiments and Simulation (2) Algorithm with Variable Window Compression Quality vs Tolerable variation of error 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. TemperatureHumidityWind Speed Tolerable Error Variation 0.1 Compression Rate15.09%75.92%64.21% Restitution Rate99.98%100%99.80% Restitution Rate This table shows that the majority of the values reconstituted by the evaluation of the polynomials will be in the specified margin

B.KECHAR WWSN – Marrakech – June 4, /32 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. Experimental DataTemperatureHumidityWind Speed ASFW Algorithm 78 %27.55 %83.37 %80.83 % ASVW Algorithm %15.09 %75.92 %64.21 %

B.KECHAR WWSN – Marrakech – June 4, /32 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

B.KECHAR WWSN – Marrakech – June 4, /32 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.

B.KECHAR WWSN – Marrakech – June 4, /32 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)

B.KECHAR WWSN – Marrakech – June 4, /32 Questions & remarks Thanks for your attention. Using Polynomial Approximation as Compression and Aggregation Technique in Wireless Sensor Networks