BASiCS Group

1
A Distributed and Adaptive Signal Processing
Approach to Reducing Energy Consumption in Sensor
Networks

• Jim Chou, Dragan Petrovic, Kannan Ramchandran
• April 2, 2003

2
Overview

• Introduction and Motivation
• Distributed Source Coding Concepts
• Application of Distributed Source Coding to
  Sensor Networks
• Simulation Results
• Conclusion

3
Motivation
X
X
Problem Nodes in a sensor network have finite
battery life, and excessive power usage can lead
to their death.
4
Motivation

• Many sensors have highly correlated data that is
  slowly varying.
• How do we exploit correlation structure with
  low-power algorithms?

5
Distributed Compression
Example X is correlated to Y dH(X,Y)lt1
3 bits
X
3 bits
Y
6
Distributed Compression
Example X is correlated to Y dH(X,Y)lt1
? bits
3 bits
X
Lets cheat!
Y
7
Distributed Compression Illustrative Example (
binary case)
Example When X0 1 0, Y can equally likely
be 0 1 0, 0 1 1, 0 0 0, 1 1 0.

• X and Y are correlated.
• Y is available at
• encoder and decoder.

X
X
Decoder
Encoder
SYSTEM-1
0 0 0 0 0 1 0 1 0 1 0 0
Need 2 bits to index this.
XY
8
Distributed Compression
Example X is correlated to Y dH(X,Y)lt1
? bits
3 bits
X
You cant cheat!
Y
9

X and Y are correlated. Y is available to
only the decoder.
X
X
Decoder
Encoder
Y
SYSTEM-2
What is the best one can do?
10
Source Coding with Side Information

X
Encoder
Decoder
X
U Codebook
Y

• Using Slepian-Wolf coding, without access to Y,
  X can be compressed using H(XY) bits!
• Same compression performance if X were
  compressed with access to Y

11
Interesting case Gaussian Source Coding with
Side Information
X Y Z
Example

X
M
M
X
Encoder
Decoder
Y

• It was shown (Wyner-Ziv 76) that the compression
  rate is same as the
• case where the encoder also has access to the
  side information (under
• assumption of Z being i.i.d. Gaussian).

12
Code Constructions

• Obvious construction Use bit to index blue and
  green codebook in each dimension.

Blue 0 Green 1
Send a 1 to the decoder
13
Code Constructions

• Obvious construction Use bit to index blue and
  green codebook in each dimension.

Blue 0 Green 1
Receive a 1 at the decoder. Only look at green
codepoints.
14
Distributed Compression

• Practical Constructions for fixed correlation
• Pradhan and Ramchandran, Proc. of DCC, March 99
• Wang and Orchard, Proc. of DCC, March 01
• Aaron and Girod, Proc. of DCC, March 02
• Zamir, Shamai, and Erez, Trans. on IT, June 02
• Chou, Pradhan and Ramchandran, Proc. of DCC,
  March 03

15
Challenges of Real World

• Theory says what is possible given the
  correlation.
• Existing work for codes that approach bounds when
  correlation is known and fixed.
• How does one find the correlation?
• How to design codes for changing correlation?

16
Sensor Networks Tree-Structured Code

• Depth of tree specifies number of bits used for
  encoding

D
0
1
4D
4D
0
1
0
1
Y

• Path in the tree specifies the encoded value.
• Can tolerate 2i-1D of correlation noise using an
  ith level codebook
• Can add binary error correction codes to each
  level to improve compression performance!

17
Sensor Networks Setup

1. Controller receives uncoded data from sensors
2. Breaks them up into clusters s.t. nodes within
   cluster are highly correlated
3. Tells each cluster what code-book to use

18
Sensor Networks Compression Rate?

• Sensor nodes measure X, data controller node has
  Y

• Controller needs to estimate number of bits, i,
  it needs from sensor nodes for X.

X Y N N correlation noise
19
Sensor Networks
X1
X2
X3
X4
Received Data
Side Info
X1
a11X1,-1
X2
a21X1 a22X2,-1
X5
X3
a31X1a32X2 a33X3,-1
X4
a41X1a42X2a43X3 a44X4,-1
X5
a51X1a52X2a53X3a54X4 a55X5,-1
20
Sensor Networks Adaptation Algorithm (LMS)

• U(t) (MK)x1 input at time t
• W(t) 1x(MK) input of weighting coeff.
• Y(t) W(t)T U(t)
• Use coset decoding to find X(t)
• E(t) X(t) Y(t)
• W(t1) W(t) mE(t)U(t)

21
Simulation Setup

• Collected data from PicoRadio test-bed nodes
• 5 light,
• 5 temperature,
• 5 humidity sensors
• Data was collected and used for testing real-time
  algorithms

22
Simulations

• Avg. Temp Savings 66.6
• Avg. Humidity Savings 44.9
• Avg. Light Savings 11.7

Correlation Noise
Time
23
Future Work

• Explore trade-off between latency and compression
• Explore trade-off between robustness and
  compression
• Explore universal prediction algorithms to
  exploit wide range of correlation structures.

24
Conclusion

• Predicting and exploiting correlation
• Exploit spatial and temporal correlation
  (increase robustness)
• Heavy computation (clustering, correlation) at
  centralized location
• Low requirements on sensor nodes