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Dr. Sudharman K. Jayaweera and Amila Kariyapperuma ECE Department University of New Mexico. Distributed & adaptive Data compression in wireless Sensor Networks. Ankur Sharma Department of ECE Indian Institute of Technology, Roorkee. 5 th July,2007. - PowerPoint PPT Presentation
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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…..