On the Feedback Capacity of Stationary Gaussian Channels
Abstract
Description
The capacity of stationary additive Gaussian noise channels with feedback is characterized as the solution to a variational problem. Toward this end, it is proved that the optimal feedback coding scheme is stationary. 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 scheme achieves the feedback capacity for the first-order autoregressive moving-average Gaussian channel, resolving a long-standing open problem studied by Butman, Schalkwijk--Tiernan, Wolfowitz, Ozarow, Ordentlich, Yang--Kavcic--Tatikonda, and others.
11 pages, v2: corrected a few typos, 43rd Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, USA, Sept. 28-30, 2005
11 pages, v2: corrected a few typos, 43rd Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, USA, Sept. 28-30, 2005