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 (MACs). 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.
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