### Abstract

Universal lossy source coding with the logarithmic loss distortion criterion is studied. Bounds on the non-asymptotic fundamental limit of fixed-length universal coding with respect to a family of distributions are derived. These bounds generalize the well-known minimax bounds for universal lossless source coding. The asymptotic behavior of the resulting optimization problem is studied for a family of i.i.d. sources with a finite alphabet size, and is characterized up to a constant. The redundancy of memoryless sources behaves like k/2 log n, where n is the blocklength and k is the number of degrees of freedom in the parameter space. The impact of the coding rate is on the constant term: higher compression rate effectively reduces the volume of the parameter uncertainty set.

Original language | English (US) |
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Title of host publication | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1157-1161 |

Number of pages | 5 |

ISBN (Electronic) | 9781509040964 |

DOIs | |

State | Published - Aug 9 2017 |

Event | 2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017 |

### Publication series

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

### Other

Other | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |
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Country | Germany |

City | Aachen |

Period | 6/25/17 → 6/30/17 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*2017 IEEE International Symposium on Information Theory, ISIT 2017*(pp. 1157-1161). [8006710] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006710