TY - GEN

T1 - Arimoto-Rényi conditional entropy and Bayesian hypothesis testing

AU - Sason, Igal

AU - Verdú, Sergio

N1 - Funding Information:
This work has been supported by the Israeli Science Foundation (ISF) under Grant 12/12, by ARO-MURI contract number W911NF-15-1-0479 and in part by the Center for Science of Information, an NSF Science and Technology Center under Grant CCF-0939370.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - This paper gives upper and lower bounds on the minimum error probability of Bayesian M-ary hypothesis testing in terms of the Arimoto-Rényi conditional entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon conditional entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano's inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano's inequality, allowing M to be infinite, a lower bound on the Arimoto-Rényi conditional entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto-Rényi conditional entropy.

AB - This paper gives upper and lower bounds on the minimum error probability of Bayesian M-ary hypothesis testing in terms of the Arimoto-Rényi conditional entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon conditional entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano's inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano's inequality, allowing M to be infinite, a lower bound on the Arimoto-Rényi conditional entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto-Rényi conditional entropy.

KW - Arimoto-Rényi conditional entropy

KW - Fano's inequality

KW - Hypothesis testing

KW - Information measures

KW - Minimum probability of error

KW - Rényi divergence

UR - http://www.scopus.com/inward/record.url?scp=85034086240&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034086240&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8007073

DO - 10.1109/ISIT.2017.8007073

M3 - Conference contribution

AN - SCOPUS:85034086240

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2965

EP - 2969

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -