### Abstract

This paper studies the minimum achievable source coding rate as a function of blocklength n and probability \epsilon that the distortion exceeds a given level d. Tight general achievability and converse bounds are derived that hold at arbitrary fixed blocklength. For stationary memoryless sources with separable distortion, the minimum rate achievable is shown to be closely approximated by R(d) + √V(d)\nQ ^{-1}(∈), where R(d) is the rate-distortion function, V(d) is the rate dispersion, a characteristic of the source which measures its stochastic variability, and Q ^{-1} is the inverse of the standard Gaussian complementary cumulative distribution function.

Original language | English (US) |
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Article number | 6145679 |

Pages (from-to) | 3309-3338 |

Number of pages | 30 |

Journal | IEEE Transactions on Information Theory |

Volume | 58 |

Issue number | 6 |

DOIs | |

State | Published - 2012 |

### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Keywords

- Achievability
- Shannon theory
- converse
- finite blocklength regime
- lossy source coding
- memoryless sources
- rate distortion

## Fingerprint Dive into the research topics of 'Fixed-length lossy compression in the finite blocklength regime'. Together they form a unique fingerprint.

## Cite this

Kostina, V., & Verdú, S. (2012). Fixed-length lossy compression in the finite blocklength regime.

*IEEE Transactions on Information Theory*,*58*(6), 3309-3338. [6145679]. https://doi.org/10.1109/TIT.2012.2186786