Entropy functions and determinant inequalities

IEEE International Symposium on Information Theory - Proceedings

Volumn , Issue , 2012, Pages 1251-1255

  Chan, Terence ^a   Guo, Dongning ^b   Yeung, Raymond ^c  

^a UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

^b Northwestern University   (United States)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Entropy; Gaussian distribution; rank functions

Indexed keywords

CONVEX CONE; ENTROPIC FUNCTION; ENTROPY FUNCTION; GAUSSIAN RANDOM VARIABLE; OUTER BOUNDS; POSITIVE-DEFINITE MATRICES; RANK FUNCTIONS;

CONES; GAUSSIAN DISTRIBUTION; INFORMATION THEORY;

ENTROPY;

EID: 84867512803     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2012.6283057     Document Type: Conference Paper

References (15)

1. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Wiley, 2006.
2. T. Cover, "Determinant inequalities via information theory," SIAM. J. Matrix Anal. & Appl., 9(3), pp.384-392, 1988.
3. R. W. Yeung, "A framework for linear information inequalities," IEEE Trans. Inform. Theory, vol. 43, no. 6, pp. 1924-1934, Nov 1997.
4. B. Hassibi and S. Shadbakht, "The entropy region for three gaussian random variables," in Information Theory, 2008. ISIT 2008. IEEE International Symposium on, july 2008, pp. 2634-2638.
5. R. W. Yeung, Information Theory and Network Coding, Springer 2008.
6. T. S. Han, "Nonnegative entropy measures of multivariate symmetric correlations," Inform. Contr., 36: 133-156, 1978.
7. T. H. Chan, "Balanced information inequalities," IEEE Trans. Inform. Theory, vol. 49, pp. 3261-3267, 2003.
8. A. Rényi, Probability Theory. Budapest, Hungary: North Holland - Academiai Kiado, 1970.
9. m," available online at https://www.math.lsu.edu/ kwiboo1/talkpaper.pdf, 2010.
10. L. Guille, T. H. Chan, and A. Grant, "The minimal set of ingleton inequalities," IEEE Trans. Inform. Theory, vol. 57, pp. 1849-1864, 2011.
11. A. W. Ingleton, "Representation of matroids." London: Academic Press, 1971, pp. 149-167.
12. R. Dougherty, C. Freiling, and K. Zeger, "Linear rank inequalities on five or more variables," Arxiv preprint cs.IT/0910.0284v3, 2009.
13. R. Kinser, "New inequalities for subspace arrangements," J. Combin. Theory Ser. A, 2010.
14. T. Chan, A. Grant, and D. Pflüger, "Truncation technique for characterising linear polymatroids," IEEE Trans. Information Theory, pp. 6364-6378, Oct 2011
15. Z. Zhang and R. W. Yeung, "On the characterization of entropy function via information inequalities," IEEE Trans. Inform. Theory, vol. 44, pp. pp. 1440-1452, 1998.