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. I. INTRODUCTIONThe standard assumption in the classical control theory is that data transmission required by the algorithm can be performed with infinite precision. However due to the growth in communication technology, it is becoming more common to employ digital finite capacity networks for exchange of information between plant components. Examples concern complex dynamical processes like advanced aircraft, spacecraft, automotive, industrial and defence systems, arrays of microactuators, and power control in mobile communication. Bandwidths communication constraints are often major obstacles to control system design by means of the classical theory. For instance as was shown in [20], design of control systems for platoons of underwater vehicles strongly highlights the need for control strategies that address explicitly the bandwidth limitation on communication between vehicles, which is severely restricted underwater. All these emerging applications motivate development of a new chapter of control theory that deals with networked systems and combines together the control and communication issues, taking into account all the limitations on communication between sensors, controllers, and actuators.Recently there was a good deal of research activity in this field; e.g., see [1], [3], [5-8], [13], [14], [16], [17], [21], [22]. Various schemes were proposed for stabilization and estimation via a limited capacity channel. The focus was on the channel quantization effects, and perfect (noiseless and undelayed) discrete channels were considered. This is in a sharp contrast with the classic communication theory, where limited capacity channels are modelled in terms of not only quantization effects but also channel errors and time delays. Moreover, many of the major results in this theory

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