Feedback Capacity of OU-Colored AWGN Channels

We derive an explicit formula of the feedback capacity for a continuous-time OU-colored AWGN channel. Among many others, this result shows that at least in some cases, the continuous-time Schalkwijk-Kailath coding scheme achieves the feedback capacity for such a channel, and feedback may not increase the capacity of a continuous-time ACGN channel even if the noise process is colored.