### Abstract

In this paper, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than η_{n} and we introduce the ε-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ε. Then we show that the ε-achievability of variable-length codes is essentially equivalent to the ε-achievability of fixed-length codes for general sources. Moreover we show the condition of ε-achievability for some restricted sources given ε.

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

Title of host publication | IEEE International Symposium on Information Theory - Proceedings |

Pages | 441-445 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2007 |

Event | 2007 IEEE International Symposium on Information Theory, ISIT 2007 - Nice Duration: 2007 Jun 24 → 2007 Jun 29 |

### Other

Other | 2007 IEEE International Symposium on Information Theory, ISIT 2007 |
---|---|

City | Nice |

Period | 07/6/24 → 07/6/29 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE International Symposium on Information Theory - Proceedings*(pp. 441-445). [4557265] https://doi.org/10.1109/ISIT.2007.4557265

**On the ∈-overflow probability of lossless codes.** / Nomura, Ryo; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

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

*IEEE International Symposium on Information Theory - Proceedings.*, 4557265, pp. 441-445, 2007 IEEE International Symposium on Information Theory, ISIT 2007, Nice, 07/6/24. https://doi.org/10.1109/ISIT.2007.4557265

}

TY - GEN

T1 - On the ∈-overflow probability of lossless codes

AU - Nomura, Ryo

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeichi

PY - 2007

Y1 - 2007

N2 - In this paper, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than ηn and we introduce the ε-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ε. Then we show that the ε-achievability of variable-length codes is essentially equivalent to the ε-achievability of fixed-length codes for general sources. Moreover we show the condition of ε-achievability for some restricted sources given ε.

AB - In this paper, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than ηn and we introduce the ε-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ε. Then we show that the ε-achievability of variable-length codes is essentially equivalent to the ε-achievability of fixed-length codes for general sources. Moreover we show the condition of ε-achievability for some restricted sources given ε.

UR - http://www.scopus.com/inward/record.url?scp=51649107856&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649107856&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2007.4557265

DO - 10.1109/ISIT.2007.4557265

M3 - Conference contribution

AN - SCOPUS:51649107856

SN - 1424414296

SN - 9781424414291

SP - 441

EP - 445

BT - IEEE International Symposium on Information Theory - Proceedings

ER -