Young-Han Kim
IEEE Transactions on Information Theory, vol. 56, no. 1, pp. 57–85, January 2010.
Preliminary results appeared in Proceedings of IEEE International Symposium on Information Theory, pp. 59–63, Seattle, Washington, July 2006.
The feedback capacity of additive stationary Gaussian noise channels
is characterized as the solution to a variational problem in the noise
power spectral density. When specialized to the first-order
autoregressive moving-average noise spectrum, this variational
characterization yields a closed-form expression for the feedback
capacity. In particular, this result shows that the celebrated
Schalkwijk–Kailath coding achieves the feedback capacity for the
first-order autoregressive moving-average Gaussian channel, positively
answering a long-standing open problem studied by Butman,
Schalkwijk–Tiernan, Wolfowitz, Ozarow, Ordentlich,
Yang–Kavcic–Tatikonda, and others. More generally, it is shown that
a -dimensional generalization of the Schalkwijk–Kailath coding
achieves the feedback capacity for any autoregressive moving-average
noise spectrum of order
. Simply put, the optimal transmitter
iteratively refines the receiver's knowledge of the intended
message. This development reveals intriguing connections between
estimation, control, and feedback communication.