## Abstract

In rate-distortion theory, three main types of distortion constraints have been popular: average, pointwise, and excess probability (aka-fidelity). A new setup is proposed here, which is suitable for fixed-length codes and constrains the distribution (profile) of distortions. This is accomplished by imposing multiple constraints on excess-distortion probabilities as well as an optional constraint on average distortion. We show that coding redundancy for compressing discrete memoryless sources is upper-bounded by R_{2}/√n + log n/2n + O(log log n/n) + R_{4} + o(1) where n is the block length, R_{2} the second-order coding rate, and R_{4} a constant. For the special case of coding with a single-fidelity constraint, R_{2} = √V Q^{-1}() where V is the source rate-dispersion function, and Q is the tail probability of a normal random variable. The upper bound is proved using a random coding scheme and deriving exact asymptotics for the probability of distortion balls with input type dependent radius.

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 | 3215-3219 |

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 |

### Other

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

City | Aachen |

Period | 6/25/17 → 6/30/17 |

## ASJC Scopus subject areas

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