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Fundamental limits of distributed tracking

Kostina, Victoria and Hassibi, Babak (2020) Fundamental limits of distributed tracking. In: 2020 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 2438-2443. ISBN 978-1-7281-6432-8. https://resolver.caltech.edu/CaltechAUTHORS:20191213-102421150

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Abstract

Consider the following communication scenario. An n-dlmensional source with memory is observed by K isolated encoders via parallel channels, who causally compress their observations to transmit to the decoder via noiseless rate-constrained links. At each time instant, the decoder receives K new codewords from the observers, combines them with the past received codewords, and produces a minimum- distortion estimate of the latest block of n source symbols. This scenario extends the classical one-shot CEO problem to multiple rounds of communication with communicators maintaining memory of the past.We prove a coding theorem showing that the minimum asymptotically (as n → ∞) achievable sum rate required to achieve a target distortion is equal to the directed mutual information from the observers to the decoder minimized subject to the distortion constraint and the separate encoding constraint. For the Gauss-Markov source observed via K parallel AWGN channels, we solve that minimal directed mutual information problem, thereby establishing the minimum asymptotically achievable sum rate. Finally, we explicitly bound the rate loss due to a lack of communication among the observers; that bound is attained with equality in the case of identical observation channels.The general coding theorem is proved via a new nonasymptotic bound that uses stochastic likelihood coders and whose asymptotic analysis yields an extension of the Berger-Tung inner bound to the causal setting. The analysis of the Gaussian case is facilitated by reversing the channels of the observers.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT44484.2020.9174006DOIArticle
https://arxiv.org/abs/1910.02534arXivDiscussion Paper
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2020 IEEE. This work was supported in part by the National Science Foundation (NSF) under grants CCF-1751356 and CCF-1817241. The work of Babak Hassibi was supported in part by the NSF under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, and by King Abdullah University of Science and Technology.
Funders:
Funding AgencyGrant Number
NSFCCF-1751356
NSFCCF-1817241
NSFCNS-0932428
NSFCCF-1018927
NSFCCF-1423663
NSFCCF-1409204
Qualcomm Inc.UNSPECIFIED
JPL President and Director's FundUNSPECIFIED
King Abdullah University of Science and Technology (KAUST)UNSPECIFIED
Subject Keywords:CEO problem, Berger-Tung bound, distributed source coding, causal rate-distortion theory, Gauss-Markov source, LQG control
Record Number:CaltechAUTHORS:20191213-102421150
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191213-102421150
Official Citation:V. Kostina and B. Hassibi, "Fundamental limits of distributed tracking," 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 2020, pp. 2438-2443, doi: 10.1109/ISIT44484.2020.9174006
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100285
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:16 Dec 2019 15:25
Last Modified:28 Aug 2020 18:16

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