### Abstract

We derive a general formula of the minimum achievable rate for fixed-to-variable length coding with a regular cost function by allowing the error probability up to a constant ϵ. For a fixed-to-variable length code, we call the set of source sequences that can be decoded without error the dominant set of source sequences. For any two regular cost functions, it is revealed that the dominant set of source sequences for a code attaining the minimum achievable rate with a cost function is also the dominant set for a code attaining the minimum achievable rate with the other cost function. We also give a general formula of the second-order minimum achievable rate.

Original language | English |
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Title of host publication | Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 16-20 |

Number of pages | 5 |

ISBN (Electronic) | 9784885523090 |

Publication status | Published - 2017 Feb 2 |

Externally published | Yes |

Event | 3rd International Symposium on Information Theory and Its Applications, ISITA 2016 - Monterey, United States Duration: 2016 Oct 30 → 2016 Nov 2 |

### Publication series

Name | Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016 |
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### Other

Other | 3rd International Symposium on Information Theory and Its Applications, ISITA 2016 |
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Country | United States |

City | Monterey |

Period | 16/10/30 → 16/11/2 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Hardware and Architecture
- Information Systems
- Signal Processing
- Library and Information Sciences

### Cite this

*Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016*(pp. 16-20). [7840377] (Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016). Institute of Electrical and Electronics Engineers Inc..

**Variable-length coding with cost allowing non-vanishing error probability.** / Yagi, Hideki; Nomura, Ryo.

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

*Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016.*, 7840377, Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016, Institute of Electrical and Electronics Engineers Inc., pp. 16-20, 3rd International Symposium on Information Theory and Its Applications, ISITA 2016, Monterey, United States, 16/10/30.

}

TY - GEN

T1 - Variable-length coding with cost allowing non-vanishing error probability

AU - Yagi, Hideki

AU - Nomura, Ryo

PY - 2017/2/2

Y1 - 2017/2/2

N2 - We derive a general formula of the minimum achievable rate for fixed-to-variable length coding with a regular cost function by allowing the error probability up to a constant ϵ. For a fixed-to-variable length code, we call the set of source sequences that can be decoded without error the dominant set of source sequences. For any two regular cost functions, it is revealed that the dominant set of source sequences for a code attaining the minimum achievable rate with a cost function is also the dominant set for a code attaining the minimum achievable rate with the other cost function. We also give a general formula of the second-order minimum achievable rate.

AB - We derive a general formula of the minimum achievable rate for fixed-to-variable length coding with a regular cost function by allowing the error probability up to a constant ϵ. For a fixed-to-variable length code, we call the set of source sequences that can be decoded without error the dominant set of source sequences. For any two regular cost functions, it is revealed that the dominant set of source sequences for a code attaining the minimum achievable rate with a cost function is also the dominant set for a code attaining the minimum achievable rate with the other cost function. We also give a general formula of the second-order minimum achievable rate.

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UR - http://www.scopus.com/inward/citedby.url?scp=85015252190&partnerID=8YFLogxK

M3 - Conference contribution

T3 - Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016

SP - 16

EP - 20

BT - Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -