### Abstract

Hayashi and Matsumoto gave two lower bounds for the secrecy exponent for wiretap channels in 2011 and 2016. They proved that the latter exponent function is greater than or equal to the former one for any positive rate, input distribution and conditional probability of wiretapper's channel. In this paper, we give a new and simple proof of the inequality between the two exponent functions. To prove the inequality we use non-negativity of Kullback-Leibler distance together with a lemma that was introduced by Arimoto to derive a computation algorithm for error and correct decoding probability exponent for discrete memoryless channels.

Original language | English |
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Title of host publication | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 747-751 |

Number of pages | 5 |

ISBN (Electronic) | 9784885523182 |

DOIs | |

Publication status | Published - Mar 8 2019 |

Event | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 - Singapore, Singapore Duration: Oct 28 2018 → Oct 31 2018 |

### Publication series

Name | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |
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### Conference

Conference | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 |
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Country | Singapore |

City | Singapore |

Period | 10/28/18 → 10/31/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Information Systems

### Cite this

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018*(pp. 747-751). [8664377] (Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ISITA.2018.8664377

**A new proof of an inequality between two secrecy exponents.** / Ukyo, Michiwaki; Jitsumatsu, Yutaka.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018.*, 8664377, Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018, Institute of Electrical and Electronics Engineers Inc., pp. 747-751, 15th International Symposium on Information Theory and Its Applications, ISITA 2018, Singapore, Singapore, 10/28/18. https://doi.org/10.23919/ISITA.2018.8664377

}

TY - GEN

T1 - A new proof of an inequality between two secrecy exponents

AU - Ukyo, Michiwaki

AU - Jitsumatsu, Yutaka

PY - 2019/3/8

Y1 - 2019/3/8

N2 - Hayashi and Matsumoto gave two lower bounds for the secrecy exponent for wiretap channels in 2011 and 2016. They proved that the latter exponent function is greater than or equal to the former one for any positive rate, input distribution and conditional probability of wiretapper's channel. In this paper, we give a new and simple proof of the inequality between the two exponent functions. To prove the inequality we use non-negativity of Kullback-Leibler distance together with a lemma that was introduced by Arimoto to derive a computation algorithm for error and correct decoding probability exponent for discrete memoryless channels.

AB - Hayashi and Matsumoto gave two lower bounds for the secrecy exponent for wiretap channels in 2011 and 2016. They proved that the latter exponent function is greater than or equal to the former one for any positive rate, input distribution and conditional probability of wiretapper's channel. In this paper, we give a new and simple proof of the inequality between the two exponent functions. To prove the inequality we use non-negativity of Kullback-Leibler distance together with a lemma that was introduced by Arimoto to derive a computation algorithm for error and correct decoding probability exponent for discrete memoryless channels.

UR - http://www.scopus.com/inward/record.url?scp=85063896117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063896117&partnerID=8YFLogxK

U2 - 10.23919/ISITA.2018.8664377

DO - 10.23919/ISITA.2018.8664377

M3 - Conference contribution

AN - SCOPUS:85063896117

T3 - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

SP - 747

EP - 751

BT - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -