  In the context of control and estimation under information constraints,
restoration entropy measures the minimal required data rate above which the
state of a system can be estimated so that the estimation quality does not
degrade over time and, conversely, can be improved. The remote observer here is
assumed to receive its data through a communication channel of finite bit-rate
capacity. In this paper, we provide a new characterization of the restoration
entropy which does not require to compute any temporal limit, i.e., an
asymptotic quantity. Our new formula is based on the idea of finding a specific
Riemannian metric on the state space which makes the metric-dependent upper
estimate of the restoration entropy as tight as one wishes.
