Fundamental limits of distributed tracking
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Consider the following communication scenario. A Gauss-Markov source is observed by K isolated observers via independent AWGN 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 mean-square error running estimate of the source. This is a causal version of the Gaussian CEO problem. We determine the minimum asymptotically achievable sum rate required to achieve a given mean-square error, which is stated as an optimization problem over K parameters. We give an explicit expression for the symmetrical case, and compute the limit of the sum rate as K →∞, which turns out to be finite and nontrivial. Furthermore, using a suboptimal waterfilling allocation among the K parameters, we explicitly bound the loss due to a lack of cooperation among the observers; that bound is attained with equality in the symmetrical case.
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