On Gaussian feedback capacity

Author

Dembo, Amir

Author_Institution

Inf. Syst. Lab., Stanford Univ., CA, USA

Volume

35

Issue

5

fYear

1989

fDate

9/1/1989 12:00:00 AM

Firstpage

1072

Lastpage

1076

Abstract

M. Pinsker and P. Ebert (Bell Syst. Tech. J., p.1705-1712, Oct.1970) proved that in channels with additive Gaussian noise, feedback at most doubles the capacity. Recently, T. Cover and S. Pombra (ibid., vol.35, no.1, p.37-43, Jan.1989) proved that feedback at most adds half a bit per transmission. Following their approach, the author proves that in the limit as signal power approaches either zero (very low SNR) or infinity (very high SNR), feedback does not increase the finite block-length capacity (which for nonstationary Gaussian channels replaces the standard notion of capacity that may not exist). Tighter upper bounds on the capacity are obtained in the process. Specializing these results to stationary channels, the author recovers some of the bounds recently obtained by L.H. Ozarow (to appear in IEEE Trans. Inf. Theory) using a different bounding technique

Keywords

channel capacity; feedback; information theory; additive Gaussian noise; channel capacity; feedback; finite block-length capacity; nonstationary Gaussian channels; stationary channels; upper bounds; Additive noise; Covariance matrix; Decoding; Feedback; Gaussian channels; Gaussian noise; H infinity control; Linear matrix inequalities; Signal to noise ratio; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.42223

Filename

42223