The convex-concave characteristics of Gaussian channel capacity functions

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, "Op...

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Bibliographic Details
Published in:IEEE transactions on information theory 2006-05, Vol.52 (5), p.2167-2172
Main Authors: Han Wu Chen, Yanagi, K.
Format: Article
Language:English
Subjects:
Applied sciences
Capacity
Channel capacity
Channels
Communication channels
Covariance matrix
Decoding
Exact sciences and technology
feedback
Gaussian
Gaussian channel
Gaussian channels
Gaussian noise
Inequalities
Information analysis
Information systems
Information theory
Information, signal and communications theory
Linear matrix inequalities
Mathematical analysis
Noise
Operators
Output feedback
Shannon theory
Signal processing
State feedback
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Theory
Transmission and modulation (techniques and equipments)
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Summary: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/sub n,Z/(P) and C/sub n,FB,Z/(P) are both concave functions of P, C/sub n,Z/(P) is a convex function of the noise covariance matrix and C/sub 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/sub n,FB,/spl middot//(P).
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2006.872851