Kostina, Victoria and Verdú, Sergio (2012) Fixed-Length Lossy Compression in the Finite Blocklength Regime. IEEE Transactions on Information Theory, 58 (6). pp. 3309-3338. ISSN 0018-9448. doi:10.1109/TIT.2012.2186786. https://resolver.caltech.edu/CaltechAUTHORS:20140910-113526494
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Abstract
This paper studies the minimum achievable source coding rate as a function of blocklength n and probability ϵ 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)/(n) Q^(-1)(ϵ), 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.
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| Additional Information: | © 2012 IEEE. Manuscript received March 27, 2011; accepted October 28, 2011. Date of publication February 03, 2012; date of current version May 15, 2012. This work was supported in part by the National Science Foundation under Grant CCF-10- 16625 and Grant CCF-09-39370. The work of V. Kostina was supported in part by the Natural Sciences and Engineering Research Council of Canada. Portions of this paper were presented at the 2011 IEEE International Symposium on Information Theory, and at the 2011 IEEE Information Theory Workshop. | ||||||||||||
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| Subject Keywords: | Achievability, converse, finite blocklength regime, lossy source coding, memoryless sources, rate distortion, Shannon theory | ||||||||||||
| Issue or Number: | 6 | ||||||||||||
| DOI: | 10.1109/TIT.2012.2186786 | ||||||||||||
| Record Number: | CaltechAUTHORS:20140910-113526494 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20140910-113526494 | ||||||||||||
| Official Citation: | Kostina, V.; Verdu, S., "Fixed-Length Lossy Compression in the Finite Blocklength Regime," Information Theory, IEEE Transactions on , vol.58, no.6, pp.3309-3338, June 2012 doi: 10.1109/TIT.2012.2186786 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 49544 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||
| Deposited On: | 10 Sep 2014 19:49 | ||||||||||||
| Last Modified: | 10 Nov 2021 18:45 |
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