### Abstract

In this letter, 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 e-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 ∈. Then we show that the e-achievability of variable-length codes is essentially equivalent to the e-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of e-achievability for some restricted sources given ∈.

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

Pages (from-to) | 2965-2970 |

Number of pages | 6 |

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

Volume | E90-A |

Issue number | 12 |

DOIs | |

Publication status | Published - 2007 Dec |

### Fingerprint

### Keywords

- Error probability
- Fixed-length codes
- Overflow probability
- Variable-length codes

### ASJC Scopus subject areas

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

### Cite this

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

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E90-A, no. 12, pp. 2965-2970. https://doi.org/10.1093/ietfec/e90-a.12.2965

}

TY - JOUR

T1 - A note on the ∈-overflow probability of lossless codes

AU - Nomura, Ryo

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeichi

PY - 2007/12

Y1 - 2007/12

N2 - In this letter, 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 e-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 ∈. Then we show that the e-achievability of variable-length codes is essentially equivalent to the e-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of e-achievability for some restricted sources given ∈.

AB - In this letter, 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 e-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 ∈. Then we show that the e-achievability of variable-length codes is essentially equivalent to the e-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of e-achievability for some restricted sources given ∈.

KW - Error probability

KW - Fixed-length codes

KW - Overflow probability

KW - Variable-length codes

UR - http://www.scopus.com/inward/record.url?scp=68249161028&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68249161028&partnerID=8YFLogxK

U2 - 10.1093/ietfec/e90-a.12.2965

DO - 10.1093/ietfec/e90-a.12.2965

M3 - Article

AN - SCOPUS:68249161028

VL - E90-A

SP - 2965

EP - 2970

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 - 12

ER -