Title :
On the entropy of the sum and of the difference of independent random variables
Author :
Lapidoth, Amos ; Pete, Gábor
Author_Institution :
ETH, Zurich, Switzerland
Abstract :
We show that the entropy of the sum of independent random variables can greatly differ from the entropy of their difference. The gap between the two entropies can be arbitrarily large. This holds for regular entropies as well as differential entropies. Our results rely heavily on a result of Ruzsa, who studied sums and differences of finite sets.
Keywords :
entropy; probability; difference; entropy; finite sets; independent random variables; probabilistic method; sum; Entropy; Random variables; Difference; Differential Entropy; Entropy; Sum;
Conference_Titel :
Electrical and Electronics Engineers in Israel, 2008. IEEEI 2008. IEEE 25th Convention of
Conference_Location :
Eilat
Print_ISBN :
978-1-4244-2481-8
Electronic_ISBN :
978-1-4244-2482-5
DOI :
10.1109/EEEI.2008.4736607
