CaltechAUTHORS
  A Caltech Library Service

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

Kostina, Victoria and Verdú, Sergio (2011) Fixed-length lossy compression in the finite blocklength regime: Gaussian source. In: 2011 IEEE Information Theory Workshop (ITW). IEEE , Piscataway, NJ, pp. 457-461. ISBN 978-1-4577-0438-3 . https://resolver.caltech.edu/CaltechAUTHORS:20140910-112002771

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20140910-112002771

Abstract

For an i.i.d. Gaussian source with variance σ^2, we show that it is necessary to spend ½ 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).


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6089501PublisherArticle
http://dx.doi.org/10.1109/ITW.2011.6089501DOIArticle
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2011 IEEE. This research was supported in part by NSF under grants CCF-1016625 and CCF 09-39370. The first author was supported in part by the Natural Sciences and Engineering Research Council of Canada.
Funders:
Funding AgencyGrant Number
NSFCCF-1016625
NSFCCF 09-39370
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Subject Keywords:Shannon theory, lossy source coding, rate distortion, memoryless sources, Gaussian source, finite blocklength regime, achievability, converse, sphere covering
Record Number:CaltechAUTHORS:20140910-112002771
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140910-112002771
Official Citation:Kostina, V.; Verdu, S., "Fixed-length lossy compression in the finite blocklength regime: Gaussian source," Information Theory Workshop (ITW), 2011 IEEE , vol., no., pp.457,461, 16-20 Oct. 2011 doi: 10.1109/ITW.2011.6089501
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49543
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:10 Sep 2014 18:39
Last Modified:03 Oct 2019 07:14

Repository Staff Only: item control page