### 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 |
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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 |

### 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