Fundamental limits of distributed tracking

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 code...

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Vydáno v:Proceedings / IEEE International Symposium on Information Theory s. 2438 - 2443
Hlavní autoři: Kostina, Victoria, Hassibi, Babak
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.06.2020
Témata:
Berger-Tung bound
causal rate-distortion theory
CEO problem
Decoding
Distortion
distributed source coding
Gauss- Markov source
LQG control
Mutual information
Observers
Optimization
Rate distortion theory
Rate-distortion
Resource management
Source coding
Symbols
ISSN:2157-8117
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Shrnutí: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.
ISSN:2157-8117
DOI:10.1109/ISIT44484.2020.9174006