The convex-concave characteristics of Gaussian channel capacity functions

Author

Chen, Han Wu ; Yanagi, Kenjiro

Author_Institution

Dept. of Comput. Sci. & Eng., Southeast Univ., Nanjing, China

Volume

52

Issue

5

fYear

2006

fDate

5/1/2006 12:00:00 AM

Firstpage

2167

Lastpage

2172

Abstract

In this correspondence, we give several inherent properties of the capacity function of a Gaussian channel with and without feedback by using some operator inequalities and matrix analysis. We give a new proof method which is different from the method appearing in: K. Yanagi and H. W. Chen, "Operator inequality and its application to information theory," Taiwanese J. Math., vol. 4, no. 3, pp. 407-416, Sep. 2000. We obtain the following results: C_n,Z(P) and C_n,FB,Z(P) are both concave functions of P, C_n,Z(P) is a convex function of the noise covariance matrix and C_n,FB,Z(P) is a convex-like function of the noise covariance matrix. This new proof method is very elementary and the results shall help study the capacity of Gaussian channel. Finally, we state a conjecture concerning the convexity of C_n,FB,·(P).

Keywords

Gaussian channels; channel capacity; channel coding; concave programming; convex programming; covariance matrices; Gaussian channel capacity function; convex-concave characteristics; covariance matrix analysis; operator inequality; Channel capacity; Covariance matrix; Decoding; Gaussian channels; Gaussian noise; Information analysis; Linear matrix inequalities; Output feedback; Signal processing; State feedback; Capacity; Gaussian channel; Shannon theory; feedback;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2006.872851

Filename

1624648