A New Entropy Power Inequality for Integer-Valued Random Variables

The entropy power inequality (EPI) yields lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function yields a sharp inequality H(X + X')-H(X) >= H(X) >= 1/2 - o(1) when X, X' are independent identically distributed (i.i.d.) with high entropy. This paper provides the inequality H(X + X') -H(X) >= g(H(X)), where X, X' are arbitrary i.i.d. integer-valued random variables and where g is a universal strictly positive function on R+ satisfying g(0) = 0. Extensions to nonidentically distributed random variables and to conditional entropies are also obtained.


Published in:
Ieee Transactions On Information Theory, 60, 7, 3787-3796
Year:
2014
Publisher:
Piscataway, Institute of Electrical and Electronics Engineers
ISSN:
0018-9448
Keywords:
Laboratories:




 Record created 2014-10-23, last modified 2018-01-28


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