## Abstract

This paper considers a noisy data structure recovery problem. Specifically, the goal is to investigate the following question: Given a noisy observation of the data, according to which permutation was the original data sorted? The main focus is on scenarios where data is generated according to an isotropic Gaussian distribution, and the perturbation consists of adding Gaussian noise with diagonal scalar covariance matrix. This problem is posed within a hypothesis testing framework. First, the optimal decision criterion is characterized and shown to be identical to the hypothesis of the observation. Then, by leveraging the structure of the optimal decision criterion, the probability of error is characterized. Finally, the logarithmic behavior (i.e., the exponent) of the probability of error is derived in the regime where the dimension of the data goes to infinity.

Original language | English (US) |
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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 | 1307-1312 |

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: Jul 21 2020 → Jul 26 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 | United States |

City | Los Angeles |

Period | 7/21/20 → 7/26/20 |

### Bibliographical note

Funding Information:The work of M. Jeong and M. Cardone was supported in part by the U.S. National Science Foundation under Grant CCF-1849757. The work of A. Dytso and H. V. Poor was supported in part by the U.S. National Science Foundation under Grant CCF-1908308