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Feedback Capacity of Stationary Gaussian Channels

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1 Author(s)
Young-han Kim ; Information Systems Laboratory, Stanford University, Stanford, CA 94305, USA. Email:

The feedback capacity of additive stationary Gaussian noise channels 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, 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 k-dimensional extension of the Schalkwijk-Kailath coding scheme achieves the feedback capacity for any autoregressive moving-average noise spectrum of order k. Simply put, the optimal transmitter iteratively refines the receiver's knowledge of the intended message

Published in:

2006 IEEE International Symposium on Information Theory

Date of Conference:

9-14 July 2006