### Abstract

Standard redundancy measures the excess number of bits needed to compress a sequence as a function of the sequence's length. Since long sequences can have arbitrarily low minimum description length (MDL), even low standard redundancy can be arbitarily high compared to the sequence's MDL. By contrast, relative redundancy evaluates the excess number of bits as a function of the sequence's MDL. Hence unlike standard redundancy, low relative redundancy implies that the number of bits needed to compress any sequence is essentially the lowest possible. Results in [1] show that for iid distributions over binary alphabets, block relative redundancy essentially equals block standard redundancy while sequential relative redundancy is about twice its standard counterpart. We show that unlike binary alphabets, for larger alphabets both block and sequential relative redundancy essentially equal their standard counterparts. We also define and determine expected relative redundancy and show that it is almost same as worst-case relative redundancy.

Original language | English (US) |
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Title of host publication | Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008 |

Pages | 1940-1943 |

Number of pages | 4 |

DOIs | |

State | Published - Sep 29 2008 |

Event | 2008 IEEE International Symposium on Information Theory, ISIT 2008 - Toronto, ON, Canada Duration: Jul 6 2008 → Jul 11 2008 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8101 |

### Other

Other | 2008 IEEE International Symposium on Information Theory, ISIT 2008 |
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Country | Canada |

City | Toronto, ON |

Period | 7/6/08 → 7/11/08 |

### ASJC Scopus subject areas

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

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## Cite this

*Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008*(pp. 1940-1943). [4595327] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2008.4595327