### Abstract

Standard redundancy measures the excess number of bits required to encode a sequence of a given length when the underlying distribution is not known. Relative redundancy measures the same increase, but as a function of the sequence's minimum description length. We consider the relative redundancy of i.i.d. distributions over large alphabets and show that, like standard redundancy, relative redundancy too increases with the alphabet size. We then consider compression of patterns of i.i.d. strings. Again analogous to standard redundancy, we show that the relative redundancy of patterns of large, or even infinite alphabet i.i.d. distributions is negligible compared to the patterns' minimum description length.

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

Pages | 2672-2676 |

Number of pages | 5 |

DOIs | |

State | Published - 2006 |

Externally published | Yes |

Event | 2006 IEEE International Symposium on Information Theory, ISIT 2006 - Seattle, WA, United States Duration: Jul 9 2006 → Jul 14 2006 |

### Other

Other | 2006 IEEE International Symposium on Information Theory, ISIT 2006 |
---|---|

Country | United States |

City | Seattle, WA |

Period | 7/9/06 → 7/14/06 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE International Symposium on Information Theory - Proceedings*(pp. 2672-2676). [4036457] https://doi.org/10.1109/ISIT.2006.262138

**Relative redundancy for large alphabets.** / Orlitsky, Alon; Santhanam, Narayana; Zhang, Junan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE International Symposium on Information Theory - Proceedings.*, 4036457, pp. 2672-2676, 2006 IEEE International Symposium on Information Theory, ISIT 2006, Seattle, WA, United States, 7/9/06. https://doi.org/10.1109/ISIT.2006.262138

}

TY - GEN

T1 - Relative redundancy for large alphabets

AU - Orlitsky, Alon

AU - Santhanam, Narayana

AU - Zhang, Junan

PY - 2006

Y1 - 2006

N2 - Standard redundancy measures the excess number of bits required to encode a sequence of a given length when the underlying distribution is not known. Relative redundancy measures the same increase, but as a function of the sequence's minimum description length. We consider the relative redundancy of i.i.d. distributions over large alphabets and show that, like standard redundancy, relative redundancy too increases with the alphabet size. We then consider compression of patterns of i.i.d. strings. Again analogous to standard redundancy, we show that the relative redundancy of patterns of large, or even infinite alphabet i.i.d. distributions is negligible compared to the patterns' minimum description length.

AB - Standard redundancy measures the excess number of bits required to encode a sequence of a given length when the underlying distribution is not known. Relative redundancy measures the same increase, but as a function of the sequence's minimum description length. We consider the relative redundancy of i.i.d. distributions over large alphabets and show that, like standard redundancy, relative redundancy too increases with the alphabet size. We then consider compression of patterns of i.i.d. strings. Again analogous to standard redundancy, we show that the relative redundancy of patterns of large, or even infinite alphabet i.i.d. distributions is negligible compared to the patterns' minimum description length.

UR - http://www.scopus.com/inward/record.url?scp=39049107079&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39049107079&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2006.262138

DO - 10.1109/ISIT.2006.262138

M3 - Conference contribution

SN - 1424405041

SN - 9781424405046

SP - 2672

EP - 2676

BT - IEEE International Symposium on Information Theory - Proceedings

ER -