Fixed-length lossy compression in the finite blocklength regime: Gaussian source

Victoria Kostina, Sergio Verdu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

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 languageEnglish (US)
Title of host publication2011 IEEE Information Theory Workshop, ITW 2011
Pages457-461
Number of pages5
DOIs
StatePublished - Dec 21 2011
Event2011 IEEE Information Theory Workshop, ITW 2011 - Paraty, Brazil
Duration: Oct 16 2011Oct 20 2011

Publication series

Name2011 IEEE Information Theory Workshop, ITW 2011

Other

Other2011 IEEE Information Theory Workshop, ITW 2011
CountryBrazil
CityParaty
Period10/16/1110/20/11

All Science Journal Classification (ASJC) codes

  • Information Systems

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    Kostina, V., & Verdu, S. (2011). Fixed-length lossy compression in the finite blocklength regime: Gaussian source. In 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