### Abstract

For an i.i.d. Gaussian source with variance σ ^{2}, we show that it is necessary to spend 1/2 ln σ ^{2}/d +1/√2n Q ^{-1}(ε) O (ln n/n) nats per sample in order to reproduce n source samples within mean-square error d with probability at least 1 -ε, where Q ^{-1} (·) is the inverse of the standard Gaussian complementary cdf. The first-order term is the rate-distortion function of the Gaussian source, while the second-order term measures its stochastic variability. We derive new achievability and converse bounds that are valid at any blocklength and show that the second-order approximation is tightly wedged between them, thus providing a concise and accurate approximation of the minimum achievable source coding rate at a given fixed blocklength (unless the blocklength is very small).

Original language | English (US) |
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Title of host publication | 2011 IEEE Information Theory Workshop, ITW 2011 |

Pages | 457-461 |

Number of pages | 5 |

DOIs | |

State | Published - Dec 21 2011 |

Event | 2011 IEEE Information Theory Workshop, ITW 2011 - Paraty, Brazil Duration: Oct 16 2011 → Oct 20 2011 |

### Publication series

Name | 2011 IEEE Information Theory Workshop, ITW 2011 |
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### Other

Other | 2011 IEEE Information Theory Workshop, ITW 2011 |
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Country | Brazil |

City | Paraty |

Period | 10/16/11 → 10/20/11 |

### All Science Journal Classification (ASJC) codes

- Information Systems

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## Cite this

*2011 IEEE Information Theory Workshop, ITW 2011*(pp. 457-461). [6089501] (2011 IEEE Information Theory Workshop, ITW 2011). https://doi.org/10.1109/ITW.2011.6089501