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The paper addresses a state estimation problem involving bit-rate communication capacity constraints. A discrete-time partially observed linear system is studied. Unlike the classic theory, the sensor signals are transmitted to the estimator over a noisy digital communication channel. A recursive coder-decoder state estimation scheme is proposed and investigated. It is shown that the classic Shannon's noisy channel capacity constitutes the border separating the cases where the reliable state estimation is and, respectively, is not possible with arbitrarily high probability.