2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | O.4.3 | ||
| Paper Title | Fundamental limits of distributed tracking | ||
| Authors | Victoria Kostina, Babak Hassibi, Caltech, United States | ||
| Session | O.4: Multi-terminal Source Coding II | ||
| Presentation | Lecture | ||
| Track | Source Coding | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | Consider the following communication scenario. An $n$-dimensional 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 $n \to \infty$) 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. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
