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Achievable Distortion-Rate Regions in Distributed Estimation with WSNs

This presentation explores efficient compression-encoding techniques for sensor observations in Wireless Sensor Networks. It covers rate-constrained distributed estimation, special cases in linear models, numerical results, and conclusions regarding achievable distortion-rate regions in WSNs.

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Achievable Distortion-Rate Regions in Distributed Estimation with WSNs

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  1. May 5, 2005EE8510 Project Presentation Distortion-Rate for Non-Distributed and Distributed Estimation with WSNs Presenter: Ioannis D. Schizas 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. . • . and • . is known and full column rank Problem Statement • Linear Model: • s, n uncorrelated and Gaussian 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 • Compress-Estimate • (C-E) ii. Estimate-Compress (E-C) • Estimation errors = f (terms due to compression), =1,2

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

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

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

  8. Distributed Setup • Desirable D-R • Treat as side info. with and • MMSE and • Let and • Optimal output of encoder 1:

  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: • Determine • Retain pair of matrices with smallest distortion • Assign r(i) to the corresponding encoder • Convergence to a local minimum is guaranteed

  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!

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