### Abstract

This paper studies the fundamental limits of the minimum average length of variable-length compression when a nonzero error probability ε is tolerated. We give non-asymptotic bounds on the minimum average length in terms of Erokhin's rate-distortion function and we use those bounds to obtain a Gaussian approximation on the speed of approach to the limit which is quite accurate for all but small blocklengths: equation where Q^{-1} (·) is the functional inverse of the Q-function and V (S) is the source dispersion. A nonzero error probability thus not only reduces the asymptotically achievable rate by a factor of 1-ε, but also this asymptotic limit is approached from below, i.e. a larger source dispersion and shorter blocklengths are beneficial. Further, we show that variable-length lossy compression under excess distortion constraint also exhibits similar properties.

Original language | English (US) |
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Title of host publication | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 2679-2683 |

Number of pages | 5 |

ISBN (Print) | 9781479951864 |

DOIs | |

State | Published - 2014 |

Event | 2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States Duration: Jun 29 2014 → Jul 4 2014 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Other

Other | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |
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Country | United States |

City | Honolulu, HI |

Period | 6/29/14 → 7/4/14 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

*2014 IEEE International Symposium on Information Theory, ISIT 2014*(pp. 2679-2683). [6875320] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2014.6875320