The CEO Problem With Inter-Block Memory

Victoria Kostina, Babak Hassibi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

An n-dimensional source with memory is observed by K isolated encoders via parallel channels, who compress their observations to transmit to the decoder via noiseless rate-constrained links while leveraging their memory of the past. 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 the memory of the past. We extend the Berger-Tung inner and outer bounds to the scenario with inter-block memory, showing that the minimum asymptotically (as n → ∞) achievable sum rate required to achieve a target distortion is bounded by minimal directed mutual information problems. For the Gauss-Markov source observed via K parallel AWGN channels, we show that the inner bound is tight and solve the corresponding 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.
Original languageEnglish (US)
Pages (from-to)7752-7768
Number of pages17
JournalIEEE Transactions on Information Theory
Volume67
Issue number12
DOIs
StatePublished - Sep 10 2021
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-05-25
Acknowledgements: This work was supported by the National Science Foundation (NSF) under Grant CCF-1751356 and Grant CCF-1817241. The work of Babak Hassibi was supported in part by NSF under Grant CNS-0932428, Grant CCF-1018927, Grant CCF-1423663, and Grant CCF1409204; in part by a grant from Qualcomm Inc.; in part by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund; and in part by King Abdullah University of Science and Technology.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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