Contents Menu

The convex-concave characteristics of Gaussian channel capacity functions

IEEE Transactions on Information Theory Volume 52 Issue 5 Page 2167-2172
published_at 2006-05
2007010017.pdf
[fulltext] 254 KB
Title
The convex-concave characteristics of Gaussian channel capacity functions
Creators Chen Han Wu
Creators Yanagi Kenjiro
Creator Keywords
Capacity Feedback Gaussian channel Shannon theory
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 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).
Languages eng
Resource Type journal article
Publishers Institute of Electrical and Electronics Engineers
Date Issued 2006-05
Rights
Copyright c2006 IEEE. Reprinted from IEEE Transactions on Information Theory, vol 52, no 5, 2006, p. 2167-2172. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Yamaguchi University Library's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org.()
File Version Version of Record
Access Rights open access
Relations
[ISSN]0018-9448
[NCID]AA00667911
info:doi/10.1109/TIT.2006.872851
[isVersionOf] [URI]http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18
Schools 大学院理工学研究科(工学)