### Abstract

We consider fixed-to-variable length coding with a regular cost function by allowing the error probability up to any constant ϵ. We first derive finite-length upper and lower bounds on the average codeword cost, which are used to derive general formulas of two kinds of minimum achievable rates. 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 under a cost function is also the dominant set for a code attaining the minimum achievable rate under the other cost function. We also give general formulas of the second-order minimum achievable rates.

Original language | English |
---|---|

Pages (from-to) | 1683-1692 |

Number of pages | 10 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E100A |

Issue number | 8 |

DOIs | |

Publication status | Published - 2017 Aug 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Coding theorem
- Coding with cost
- General source
- Information spectrum
- Weak variable-length coding

### ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics

### Cite this

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

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E100A, no. 8, pp. 1683-1692. https://doi.org/10.1587/transfun.E100.A.1683

}

TY - JOUR

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

AU - Yagi, Hideki

AU - Nomura, Ryo

PY - 2017/8/1

Y1 - 2017/8/1

N2 - We consider fixed-to-variable length coding with a regular cost function by allowing the error probability up to any constant ϵ. We first derive finite-length upper and lower bounds on the average codeword cost, which are used to derive general formulas of two kinds of minimum achievable rates. 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 under a cost function is also the dominant set for a code attaining the minimum achievable rate under the other cost function. We also give general formulas of the second-order minimum achievable rates.

AB - We consider fixed-to-variable length coding with a regular cost function by allowing the error probability up to any constant ϵ. We first derive finite-length upper and lower bounds on the average codeword cost, which are used to derive general formulas of two kinds of minimum achievable rates. 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 under a cost function is also the dominant set for a code attaining the minimum achievable rate under the other cost function. We also give general formulas of the second-order minimum achievable rates.

KW - Coding theorem

KW - Coding with cost

KW - General source

KW - Information spectrum

KW - Weak variable-length coding

UR - http://www.scopus.com/inward/record.url?scp=85026661047&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026661047&partnerID=8YFLogxK

U2 - 10.1587/transfun.E100.A.1683

DO - 10.1587/transfun.E100.A.1683

M3 - Article

VL - E100A

SP - 1683

EP - 1692

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 8

ER -