TY - GEN
T1 - An improved upper bound for the most informative boolean function conjecture
AU - Ordentlich, Or
AU - Shayevitz, Ofer
AU - Weinstein, Omri
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - Suppose X is a uniformly distributed n-dimensional binary vector and Y is obtained by passing X through a binary symmetric channel with crossover probability α. A recent conjecture by Courtade and Kumar postulates that I(F(X); Y ) ≤ 1 - h(α) for any Boolean function F. So far, the best known upper bound was essentially I(F(X); Y ) ≤ (1 - 2α)2. In this paper, we derive a new upper bound that holds for all balanced functions, and improves upon the best known previous bound for α > 1 over 3.
AB - Suppose X is a uniformly distributed n-dimensional binary vector and Y is obtained by passing X through a binary symmetric channel with crossover probability α. A recent conjecture by Courtade and Kumar postulates that I(F(X); Y ) ≤ 1 - h(α) for any Boolean function F. So far, the best known upper bound was essentially I(F(X); Y ) ≤ (1 - 2α)2. In this paper, we derive a new upper bound that holds for all balanced functions, and improves upon the best known previous bound for α > 1 over 3.
UR - http://www.scopus.com/inward/record.url?scp=84985911233&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2016.7541349
DO - 10.1109/ISIT.2016.7541349
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AN - SCOPUS:84985911233
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 500
EP - 504
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -