### Abstract

Lossless variable-length source coding with codeword cost is considered for general sources. The problem setting, where we impose on unequal costs on code symbols, is called the variable-length coding with codeword cost. In this problem, the infimum of average codeword cost have already been determined for general sources. On the other hand, the overflow probability, which is defined as the probability of codeword cost being above a threshold, have not been considered yet. In this paper, we first determine the infimum of achievable threshold in the first-order sense and the second-order sense for general sources with additive memoryless codeword cost. Then, we compute it for some special sources such as i.i.d. sources and mixed sources. A generalization of the codeword cost is also discussed.

Original language | English |
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Article number | 8839856 |

Pages (from-to) | 8194-8206 |

Number of pages | 13 |

Journal | IEEE Transactions on Information Theory |

Volume | 65 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2019 Dec |

### Keywords

- Codeword cost
- general source
- information-spectrum
- overflow probability
- variable-length coding

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

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## Cite this

*IEEE Transactions on Information Theory*,

*65*(12), 8194-8206. [8839856]. https://doi.org/10.1109/TIT.2019.2941888