TY - GEN
T1 - Arimoto-Rényi conditional entropy and Bayesian hypothesis testing
AU - Sason, Igal
AU - Verdú, Sergio
N1 - Funding Information:
We gratefully acknowledge the financial support provided by the National Key Technology R&D Program (2014BAG08B01) and the projects of the NSFC (51177138,61473238,51407146).
Publisher Copyright:
© 2017 IEEE.
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
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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 -