Optimal communication systems with noiseless feedback for a binary source and white Gaussian channel

Author

Korn, Israel

Volume

15

Issue

1

fYear

1969

fDate

1/1/1969 12:00:00 AM

Firstpage

61

Lastpage

66

Abstract

The sequential and nonsequential feedback systems for a binary source, first proposed by Turin, are considered. It is shown that in both cases the optimal signals belong to the family $\\pm A (y)[1 + \\exp (\\pm y)]^{-1}$ , where $A(y)$ is arbitrary. In the sequential scheme the bound on transmission rate is achieved for any $P_{e}$ by all members of this family, and in the nonsequential scheme for small $P_{e}$ only. The optimal signals within this family, i.e., signals for which $\\alpha =$ peak power/average power is minimal, result if $A(y) = \\pm \\sqrt {\\alpha P_{av}} (1 -b e^{-|y|})$ . In the sequential case, the optimal scheme is compared with two suboptimal schemes, and the advantages of the first are demonstrated. Finally, the problem of sequential detection with time-varying thresholds is presented, and its equivalence to a problem with fixed thresholds is proved.

Keywords

Feedback communication; Sequential detection; Signal design; Channel capacity; Delay; Equations; Feedback; Gaussian channels; Gaussian noise; Information theory;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1969.1054273

Filename

1054273