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Distributed State Estimation with Bounded Errors over Multiple Access Channels
Although state estimation in networked control systems is a fundamental
problem, few efforts have been made to study distributed state estimation via
multiple access channels (MAC's). In this article, we give a characterization
of the zero-error capacity region of an M-input, single-output MAC at any
finite block-length. To this end, nonstochastic information-theoretic tools are
used to derive the converse and achievability proofs. Next, a tight condition
to be able to achieve uniformly bounded state estimation errors over such a MAC
is provided. The obtained condition establishes a connection between the
intrinsic topological entropies of the linear systems and the zero-error
capacity region of the MAC