Talks and Poster Presentations (with Proceedings-Entry):
G. Pichler, G. Koliander, E. Riegler, F. Hlawatsch:
"Entropy for Singular Distributions";
Talk: 2014 IEEE International Symposium on Information Theory (ISIT 2014),
Honolulu, HI, USA;
- 07-04-2014; in: "IEEE International Symposium on Information Theory (ISIT), 2014",
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables (which are neither discrete nor continuous) has not been available so far. Here, we propose such an extension for the practically relevant class of singular probability measures that are supported on a lower-dimensional subset of Euclidean space. We show that our entropy transforms in a natural manner under Lipschitz functions and that it conveys useful expressions of the mutual information. Potential applications of the proposed entropy definition include capacity calculations for the vector interference channel, compressed sensing in a probabilistic setting, and capacity bounds for block-fading channel models.
information entropy, information measures, mutual information, rectifiable sets, singular measures
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.