Lower bounds on the estimation error in problems of distributed computation
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Como-2009-Lower bounds on the estimation error in problems of distributed computation.pdf
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Author(s)
Como, Giacomo
Dahleh, Munther A.
Date Issued
February 2009
Journal
Information Theory and Applications Workshop, 2009
Publisher
Institute of Electrical and Electronics Engineers
Citation
Como, Giacomo, and Dahleh, Munther (2009). Lower bounds on the estimation error in problems of distributed computation. Information Theory and Applications Workshop, 2009 (Piscataway, N.J.: IEEE): 70-76. © Copyright 2009 IEEE
Version
Final published version
Abstract
Information-theoretic lower bounds on the estimation error are derived for problems of distributed computation. These bounds hold for a network attempting to compute a real-vector-valued function of the global information, when the nodes have access to partial information and can communicate through noisy transmission channels. The presented bounds are algorithm-independent, and improve on recent results by Ayaso et al., where the exponential decay rate of the mean square error was upper-bounded by the minimum normalized cut-set capacity. We show that, if the transmission channels are stochastic, the highest achievable exponential decay rate of the mean square error is in general strictly smaller than the minimum normalized cut-set capacity of the network. This is due to atypical channel realizations, which, despite their asymptotically vanishing probability, affect the error exponent.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1109/ITA.2009.5044925
