DISTRIBUTED & ADAPTIVE DATA

COMPRESSION IN WIRELESS SENSOR

NETWORKS

Dr. Sudharman K. Jayaweera and Amila Kariyapperuma

ECE Department

University of New Mexico

Ankur SharmaDepartment of ECE

Indian Institute of Technology, Roorkee

5th July,2007

Expand Your Engineering Skills (EYES), Summer Internship Program, 2007

Introduction

Wireless Sensor Networks (WSN) consist of nodes for sensingTemperaturePressureLightMagnetometerInfraredAudio/Video etc

Ad hoc WSN may require inter-sensor communication.

Problem Nodes are

of small physical dimensionsBattery operated

Major concern is energy consumption Failure of nodes due to energy depletion can

lead to Partition of sensor networkLoss of critical information

Requirement of application/system is that every node should know the data of each other node.

Related Work

Energy aware routing & efficient information processing. [Shah and Rabaey, 2002]

Local compression & probabilistic estimation schemes. [ Luo,2005]

Distributed compression & adaptive signal processing in sensor networks with a fusion center. [ Chou, 2003]

Our Approach

i bit

i biti bit

2

34

1i bit

i bit i bit

Proposed Algorithm Sensor j predicts its own reading, depending upon its

past readings and readings from other sensors.

Depending upon error between predicted value and actual value i.e.

sensor j calculates the compressed bits i using Chebyshev’s inequality method Exact error method

Code Construction

A codebook to encode data X to i bits.

One underlying codebook that is NOT changed among the sensors.

Supports multiple compression rates.

A Tree-based Codebook

0

0 01 1

1

Chebyshev’s Inequality Method To prevent decoding errors with i bits

Chebyshev bound for probability of decoding error

Required value of Value of i :

Exact Error Method To prevent decoding errors using i bits

As we know exact error in the prediction of sensor data X, number of bits are

Send extra bits also, specifying the number of bits in the message.

Encoder Sensors

X is stored as the closest representation from 2n values in the root codebook

(A/D converter).

Mapping from X to the bits that specify the subcode-book at level i is done using

Decoder Sensors Decoders receive i-bit value & code sequence

f(x). Traverse the tree starting from LSB of code

sequence to find appropriate subcode book, S. Calculates the side information Y as

Decodes the side information Y, to the closest value in S as

Correlation Tracking

Linear prediction methodAnalytically tractableOptimal when readings can be modeled as

i.i.d. Gaussian random variables. First sensor always sends its data

compressed w.r.t. its own past data. Prediction of X is

where

Least-Squares Parameter Estimation Prediction error is

Choose filter coefficients in order to minimize weighted least squares error.

Least squares filter coefficient vector at time k is given by

where

Recursive Least-Squares (RLS) Algorithm Filter coefficient computation is performed

adaptively using RLS

where

and For initialization, each sensor sends uncoded data

samples. In our approach reference sensor updates the

corresponding coefficients and sends them to all other sensors.

Decoding Errors

No decoding errors in exact error method.

In Chebyshev’s method, no of encoding bits are specified within a given probability of error and after every 100 samples.

Leads to few decoding errors, but results in higher compression.

Implementation & Performance

Simulations were performed for measurements on humidity data.

We assumed a 12 bit A/D converter with a dynamic range of [-128,128].

Simulated results for about 18,000 samples for each sensor (total of 90,000)

Sensor orderings are randomized every 500 samples.

For RLS training, first 25 samples of each sensor are transmitted without any compression.

Coefficients are updated and shared after every 500 samples.

Exact Error implementation With each code sequence, extra 4 bits to

specify the number of bits are also sent.

Decoding Error = 0 Average Energy Saving %= 43.34%

Sensor # Energy Saving% Decoding Error%

1 45.90 0

2 49.85 0

3 38.52 0

4 40.75 0

5 41.67 0

Tolerable Noise vs. Prediction Noise

Chebyshev’s Inequality method

Encoding bits are specified every 100 samples Case I: Probability of Error ( Pe )= 0.5%

Average Decoding Error % = 0.07% Average Energy Saving % = 45.74%

Sensor # Energy Saving% Decoding Error%

1 47.74 0.32

2 53.15 0.00

3 41.08 0.02

4 43.03 0.01

5 43.74 0.00

Tolerable Noise vs. Prediction Noise

Chebyshev’s Inequality method

Case II: Probability of Error ( Pe )= 1.0%

Average Decoding Error % = 0.13% Average Energy Saving % = 49.74%

Sensor # Energy Saving% Decoding Error%

1 51.91 0.32

2 57.63 0.27

3 44.92 0.02

4 46.40 0.03

5 47.84 0.00

Chebyshev’s Inequality method

Case II: Probability of Error ( Pe )= 1.5%

Average Decoding Error % = 2.29% Average Energy Saving % = 52.27%

Sensor # Energy Saving% Decoding Error%

1 54.30% 0.66%

2 59.74% 7.98%

3 47.52% 2.17%

4 49.61% 0.61%

5 50.18% 0.05%

ComparisonExact Error Method Chebyshev’s Method

ZERO probability of decoding error

Compression is low (due to extra bit information)

Strict bound

‘Instantaneous approach’

Probability of decoding error within a required bound.

Higher Compression can be achieved by varying required probability of error.

Loose bound

‘Average approach’.

Probability of Error vs. Energy Savings

For Temperature Data

Exact error methodAverage energy savings % = 56.66%Average decoding error % = 0

Chebyshev’s method ( Pe = 0.01)Average energy savings % = 66.98%Average decoding error % = 0.61%

For Light Data

Exact error methodAverage energy savings % = 33.52%Average decoding error % = 0

Chebyshev’s method ( Pe = 0.01)Average energy savings % = 19.29%Average decoding error % = 1.13%

Conclusions Energy savings achieved through our

simulations are conservative estimates of what can be achieved in practice.

Further work can be done on Better predictive models.Better probability of error bound.

Can be integrated with an energy saving-routing algorithm to increase the energy savings.

Thank You!!!!

Queries Please…..