## Abstract

Suppose that Y^{n} is obtained by observing a uniform Bernoulli random vector X^{n} through a binary symmetric channel with crossover probability α. The "most informative Boolean function" conjecture postulates that the maximal mutual information between Y^{n} and any Boolean function b(X^{n}) 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(X^{n});Y^{n}) < (n - 1) • (1 - h(α)) for any such f. Thus, in this case, the optimal function is of the form f(x^{n}) = (x_{1},...,x_{n-1}).

Original language | American 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

Funding Information:The work of WH and OO was supported by the MIT - Technion Postdoctoral Fellowship.

Publisher Copyright:

© 2017 IEEE.