Abstract
Suppose that Yn is obtained by observing a uniform Bernoulli random vector Xn through a binary symmetric channel with crossover probability α. The "most informative Boolean function" conjecture postulates that the maximal mutual information between Yn and any Boolean function b(Xn) is attained by a dictator function. In this paper, we consider the "complementary" case in which the Boolean function is replaced by f: {0, 1}n → {0,1}n, namely, an n - 1 bit quantizer, and show that I(f(Xn);Yn) < (n - 1) • (1 - h(α)) for any such f. Thus, in this case, the optimal function is of the form f(xn) = (x1,...,xn-1).
Original language | English |
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Title of host publication | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 91-95 |
Number of pages | 5 |
ISBN (Electronic) | 9781509040964 |
DOIs | |
State | Published - 9 Aug 2017 |
Externally published | Yes |
Event | 2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: 25 Jun 2017 → 30 Jun 2017 |
Publication series
Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |
Conference
Conference | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |
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Country/Territory | Germany |
City | Aachen |
Period | 25/06/17 → 30/06/17 |
Bibliographical note
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