### Abstract

This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the ϵ-variable-length resolvability. We derive the general formula of the ϵ-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint that the value of the average variational distance is smaller than or equal to a constant ϵ. Our result clarifies a dual relationship between the general formula of ϵ-variable-length resolvability and that of ϵ-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.

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 | 354-358 |

Number of pages | 5 |

ISBN (Electronic) | 9784885523182 |

DOIs | |

Publication status | Published - 2019 Mar 8 |

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

### 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 | 18/10/28 → 18/10/31 |

### ASJC Scopus subject areas

- Computer Science Applications
- Information Systems

### Cite this

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018*(pp. 354-358). [8664364] (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.2018.8664364

**Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance.** / Yoshizawa, Jun; Saito, Shota; Matsushima, Toshiyasu.

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

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018.*, 8664364, Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018, Institute of Electrical and Electronics Engineers Inc., pp. 354-358, 15th International Symposium on Information Theory and Its Applications, ISITA 2018, Singapore, Singapore, 18/10/28. https://doi.org/10.23919/ISITA.2018.8664364

}

TY - GEN

T1 - Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance

AU - Yoshizawa, Jun

AU - Saito, Shota

AU - Matsushima, Toshiyasu

PY - 2019/3/8

Y1 - 2019/3/8

N2 - This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the ϵ-variable-length resolvability. We derive the general formula of the ϵ-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint that the value of the average variational distance is smaller than or equal to a constant ϵ. Our result clarifies a dual relationship between the general formula of ϵ-variable-length resolvability and that of ϵ-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.

AB - This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the ϵ-variable-length resolvability. We derive the general formula of the ϵ-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint that the value of the average variational distance is smaller than or equal to a constant ϵ. Our result clarifies a dual relationship between the general formula of ϵ-variable-length resolvability and that of ϵ-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.

UR - http://www.scopus.com/inward/record.url?scp=85063914269&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063914269&partnerID=8YFLogxK

U2 - 10.23919/ISITA.2018.8664364

DO - 10.23919/ISITA.2018.8664364

M3 - Conference contribution

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

SP - 354

EP - 358

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

PB - Institute of Electrical and Electronics Engineers Inc.

ER -