### Abstract

The Shannon Noiseless coding theorem (the data-compression principle) asserts that for an information source with an alphabet X= { 0, …, ℓ- 1 } and an asymptotic equipartition property, one can reduce the number of stored strings (x_{0}, …, x_{n}_{-}_{1}) ∈ X^{n} to ℓ^{nh} with an arbitrary small error-probability. Here h is the entropy rate of the source (calculated to the base ℓ). We consider further reduction based on the concept of utility of a string measured in terms of a rate of a weight function. The novelty of the work is that the distribution of memory is analyzed from a probabilistic point of view. A convenient tool for assessing the degree of reduction is a probabilistic large deviation principle. Assuming a Markov-type setting, we discuss some relevant formulas and examples.

Original language | English (US) |
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Title of host publication | Analytical and Computational Methods in Probability Theory - 1st International Conference, ACMPT 2017, Proceedings |

Editors | Vladimir V. Rykov, Nozer D. Singpurwalla, Andrey M. Zubkov |

Publisher | Springer Verlag |

Pages | 309-321 |

Number of pages | 13 |

ISBN (Print) | 9783319715032 |

DOIs | |

State | Published - Jan 1 2017 |

Event | 1st International Conference Analytical and Computational Methods in Probability Theory, ACMPT 2017 - Moscow, Russian Federation Duration: Oct 23 2017 → Oct 27 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10684 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st International Conference Analytical and Computational Methods in Probability Theory, ACMPT 2017 |
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Country | Russian Federation |

City | Moscow |

Period | 10/23/17 → 10/27/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Analytical and Computational Methods in Probability Theory - 1st International Conference, ACMPT 2017, Proceedings*(pp. 309-321). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10684 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-71504-9_26