Bouabdellah KECHAR [email protected] Oran University

Using Polynomial Approximation as Compression and Aggregation Technique

in Wireless Sensor Networks

Bouabdellah KECHAR

[email protected]

Oran University

Faculty of science – Department of Computer Science

Algeria

June 4, 2007Workshop on Wireless Sensor Networks

Marrakech - Morocco

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B.KECHAR WWSN – Marrakech – June 4, 2007

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

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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

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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

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Contents

Introduction

Objective

Related works



Fixed window based


Local aggregation



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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)

IN OUT

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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

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Contents

Introduction

Objective

Related works



Fixed window based


Local aggregation



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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]

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Contents

Introduction

Objective

Related works



Fixed window based


Local aggregation



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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 approximationStone-Weierstrass theorem

Application scenario and suppositionsEvery sensor have: CPU, RAM, RADIO, protocols

Variation of error tolerated by application

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Contents

Introduction

Objective

Related works



Fixed window based


Local aggregation



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Algorithms of compression : Fixed WindowDim: number of readings by sequence

Tab: collected readings

Poly: polynomial coefficients

ni: sensor node object

VarErr: evaluation of polynomial and calculation of variation

Sensed and collected data at time tj

Dim: number of readings by sequence





m: Polynomial degree

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Variation of error







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Find a new polynomial while condition is true, otherwise save polynomial and transmit it

)1(

)()(

22

nn

EEnEVarErr

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Start Approximation using Least-Squares method







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Algorithms of compression : Variable Window






WindowMin: minimal size of time window

WindowMax: maximal size of time window

OldDegree: Degree of last approximation


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Sensed and collected data of initial window

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Initialization

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Check if the old polynomial is extensible

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A new collected value is added and the old degree is saved

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To limit the algorithm by a number of readings (WindowMax)

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Contents

Introduction

Objective

Related works



Fixed window based


Local aggregation



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Local Aggregation

Coefficient of correlation

YXYX

YXCov

*

),(,

11 , YX

n

iyixi yx

nYXCov

1

))((1

),( With

IDS tn V1 ….. Vn

Packet structureWithout compression

IDS tn P(ti)

Packet structureWith compression

Correlated polynomial Transmit juste

IDS tn

Packet structureWith compression

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Contents

Introduction

Objective

Related works



Fixed window based


Local aggregation



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Experiments and Simulation (1)

Compression ratio during one period

100Re

xradingNumbe

tsNumberCoefficiennRateCompressio

Algorithm with Fixed Window

Compression Quality vs Window SizeWith 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.

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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.

Temperature Humidity Wind Speed

Tolerable Error Variation

0.1 0.1 0.1

Compression Rate 15.09% 75.92% 64.21%

Restitution Rate 99.98% 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

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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 Data Temperature Humidity Wind Speed

ASFW Algorithm 78 % 27.55 % 83.37 % 80.83 %

ASVW Algorithm 15.14 % 15.09 % 75.92 % 64.21 %

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Contents

Introduction

Objective

Related works



Fixed window based


Local aggregation



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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.

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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)

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Questions & remarks

Thanks for your attention.

Using Polynomial Approximation as Compression and Aggregation Technique in Wireless Sensor Networks

Bouabdellah KECHAR [email protected] Oran University

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