Consider a distributed control problem with a communication
channel connecting the observer of a linear stochastic system to the controller. The observer sees only a noise-corrupted version of the state, and the goal of the controller is minimize a quadratic cost function. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b. We show a lower bound on the rate necessary to attain b, which applies as long as the system and the observation noises are jointly Gaussian. 
  
If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's estimate of the current state and the observer's estimate.