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On Rate Requirements for Achieving the Centralized Performance in Distributed Estimation

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第8期65卷 2020-2032页

作者： El Gamal, Mostafa Lai, Lifeng Worcester Polytech Inst Dept Elect & Comp Engn Worcester MA 01609 USA Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center which obtains an estimate of a parameter related to the observations of all terminals. It is well known that if the transmission rates are in the Slepian-Wolf region, the fusion center can fully recover all observations and hence can construct an estimator having the same performance as that of the centralized case. One natural question is whether Slepian-Wolf rates are necessary to achieve the same estimation performance as that of the centralized case. In this paper, we show that the answer to this question is negative. We establish our result by explicitly constructing an asymptotically minimum variance unbiased estimator that has the same performance as that of the optimal estimator in the centralized case while using information rates less than the conditions required in the Slepian-Wolf rate region. The key idea is that, instead of aiming to recover the observations at the fusion center, we design universal schemes enabling the fusion center to compute a sufficient statistic using rates outside of the Selpian-Wolf region.

关键词： Distributed learning MVUE estimation algorithm Slepian-Wolf rates universal encoding/decoding scheme

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Are Slepian-Wolf Rates Necessary for Distributed Parameter Estimation? 53

Are Slepian-Wolf Rates Necessary for Distributed Parameter E...

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53rd Annual IEEE Allerton Conference on Communication, Control, and Computing (Allerton)

作者： El Gamal, Mostafa Lai, Lifeng Worcester Polytech Inst Dept Elect & Comp Engn Worcester MA 01609 USA

ISBN: (纸本)9781509018246

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center who will obtain an estimate of a parameter related to observations of all terminals. It is well known that if the transmission rates are in the Slepian-Wolf region, the fusion center can fully recover all observations and hence can construct an estimator having the same performance as that of the centralized case. One natural question is whether Slepian-Wolf rates are necessary to achieve the same estimation performance as that of the centralized case. In this paper, we show that the answer to this question is negative. We establish our result by explicitly constructing an asymptotically minimum variance unbiased estimator (MVUE) that has the same performance as that of the optimal estimator in the centralized case while requiring information rates less than the conditions required in the Slepian-Wolf rate region.

关键词： Distributed learning MVUE Slepian-Wolf rates universal encoding/decoding scheme

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Are Slepian-Wolf Rates Necessary for Distributed Parameter Estimation?

Are Slepian-Wolf Rates Necessary for Distributed Parameter E...

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Annual Allerton Conference on Communication, Control, and Computing

作者： Mostafa El Gamal Lifeng Lai Department of Electrical and Computer Engineering Worcester Polytechnic Institute MA 01609 United States

ISBN: (纸本)9781509018253

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center who will obtain an estimate of a parameter related to observations of all terminals. It is well known that if the transmission rates are in the Slepian-Wolf region, the fusion center can fully recover all observations and hence can construct an estimator having the same performance as that of the centralized case. One natural question is whether Slepian-Wolf rates are necessary to achieve the same estimation performance as that of the centralized case. In this paper, we show that the answer to this question is negative. We establish our result by explicitly constructing an asymptotically minimum variance unbiased estimator (MVUE) that has the same performance as that of the optimal estimator in the centralized case while requiring information rates less than the conditions required in the Slepian-Wolf rate region.

关键词： Distributed learning MVUE Slepian-Wolf rates universal encoding/decoding scheme

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