Scalar estimation and control with noisy binary observations

We consider a simple one-dimensional system whose observations are sent to a state estimator over a noisy binary communication link. The interesting thing about the system is that it is unstable. The problem is to design an encoding scheme and a decoder such that the estimation error is stable. We explicitly construct a simple but efficient estimator for the binary symmetric channel (BSC). We are not aware of any such previous "codes" for the BSC. We compare our results to the nonconstructive bounds of Sahai.