### 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 |
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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 |

### Keywords

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

### ASJC Scopus subject areas

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