1 Distortion-Rate for Non-Distributed and Distributed Estimation with WSNs Presenter: Ioannis D. Schizas May 5, 2005 EE8510 Project May 5, 2005 EE8510 Project Presentation Presentation Acknowledgements: Profs. G. B. Giannakis and N. Jindal

2 Motivation and Prior Work  Energy/Bandwidth constraints in WSN call for efficient compression-encoding  Bounds on minimum achievable distortion under prescribed rate important for :  Compressing and reconstructing sensor observations Best known inner and outer bounds in [Berger-Tung’78] Iterative determination of achievable D-R region [Gastpar et. al’04]  Estimating signals (parameters) under rate constraints The CEO problem [Viswanathan et. al’97, Oohama’98, Chen et. al’04, Pandya et. al’04] Rate-constrained distributed estimation [Ishwar et. al’05]

3 Problem Statement  Linear Model:  s, n uncorrelated and Gaussian and .. .. is known and full column rank .. Goal: Determine D-R function or more strict achievable D-R regions than obvious upper bounds when estimating s under rate constraints.

4 Point-to-Point Link (Single-Sensor)  Two non-distributed encoding options  Estimation errors i.Compress-Estimate (C-E) ii. Estimate-Compress (E-C) = f (terms due to compression), =1,2

5 E-C outperforms C-E  Special Cases: Scalar case: Vector case (p=1): If If, then Matrix case: Theorem 1:, then similar ‘threshold rates’ for which

6 Optimality of Estimate-Compress  Extends the result in [Sakrison’68, Wolf-Ziv’70] in linear models & N>p. Theorem 2:

7 Numerical Results   and  EC converges faster than CE to the D-R lower bound

8 Distributed Setup  Desirable D-R  Treatas side info. with and  MMSEand  Let  Optimal output of encoder 1: and 

9 Distributed E-C  Extends [Gastpar,et.al’04] to the estimation setup  Steps of iterative algorithm:  Initialize assuming each sensor works independently  Create M random rate increments r(i) s.t.  During iteration j: Retain pair of matrices with smallest distortion  Convergence to a local minimum is guaranteed, Assign r(i) to the corresponding encoder Determine

10 Numerical Experiment SNR=2,  and  Distributed E-C yields tighter upper bound for D-R than the marginal E-C

11 Conclusions  Comparison of two encoders for estimation from a D-R perspective  D-R function for the single-sensor non-distributed setup  Optimality of the estimate-first & compress-afterwards option  Numerical determination of an achievable D-R region, or, at best the D-R function for distributed estimation with WSNs Thank You!