Encoder-controller design for control over the binary-input Gaussian channel

In this paper, we consider the problem of the joint optimization of encoder-controller for closed-loop control with state feedback over a binary-input Gaussian channel (BGC). The objective is to minimize the expected linear quadratic cost over a finite horizon. This encoder-controller optimization problem is hard in general, mostly because of the curse of dimensionality. The result of this paper is a synthesis technique for a computationally feasible suboptimal controller which exploits both the soft and hard information of the channel outputs. The proposed controller is efficient in the sense that it embraces measurement quantization, error protection and control over a finite-input infinite-output noisy channel. How to effectively implement this controller is also addressed in the paper. In particular, this is done by using Hadamard techniques. Numerical experiments are carried out to verify the promising gain offered by the combined controller, in comparison to the hard-information-based controller.