## Abstract

In this paper we consider the problem of binary hypothesis testing with finite memory systems. Let X 1 , X 2 ,. be a sequence of independent identically distributed Bernoulli random variables, with expectation p under {{\mathcal{H}}-0} and q under {{\mathcal{H}}-1}. Consider a finite-memory deterministic machine with S states that updates its state M n {1,2,., S} at each time according to the rule M n = f(M n-1 , X n ), where f is a deterministic time-invariant function. Assume that we let the process run for a very long time (n→∞), and then make our decision according to some mapping from the state space to the hypothesis space. The main contribution of this paper is a lower bound on the Bayes error probability P e of any such machine. In particular, our findings show that the ratio between the maximal exponential decay rate of P e with S for a deterministic machine and for a randomized one, can become unbounded, complementing a result by Hellman.

Original language | American English |
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Title of host publication | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1259-1264 |

Number of pages | 6 |

ISBN (Electronic) | 9781728164328 |

DOIs | |

State | Published - Jun 2020 |

Event | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2020-June |

ISSN (Print) | 2157-8095 |

### Conference

Conference | 2020 IEEE International Symposium on Information Theory, ISIT 2020 |
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Country/Territory | United States |

City | Los Angeles |

Period | 21/07/20 → 26/07/20 |

### Bibliographical note

Publisher Copyright:© 2020 IEEE.