Title :
Moment-Entropy Inequalities for a Random Vector
Author :
Lutwak, Erwin ; Yang, Deane ; Zhang, Gaoyong
Author_Institution :
Dept. of Math., Polytech. Univ. Brooklyn, NY
fDate :
4/1/2007 12:00:00 AM
Abstract :
The pth moment matrix is defined for a real random vector, generalizing the classical covariance matrix. Sharp inequalities relating the pth moment and Renyi entropy are established, generalizing the classical inequality relating the second moment and the Shannon entropy. The extremal distributions for these inequalities are completely characterized
Keywords :
covariance matrices; entropy; Renyi entropy; Shannon entropy; covariance matrix; moment-entropy inequality; random vector; AWGN; Decoding; Fading; Lattices; Notice of Violation; Phase detection; Phase modulation; Signal processing; Speech processing; Upper bound; Covariance; Renyi entropy; covariance matrix; entropy; information measure; information theory; moment; moment matrix; random vector;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2007.892780
