Fixed-Length Lossy Compression in the Finite Blocklength Regime
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 sep...
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| Published in: | IEEE transactions on information theory Vol. 58; no. 6; pp. 3309 - 3338 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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New York
IEEE
01.06.2012
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
| Online Access: | Get full text |
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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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| AbstractList | 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 ) n Q - 1 ( epsilon ) , 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 ( times ) is the inverse of the standard Gaussian complementary cumulative distribution function. 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 $R(d) + sqrt {{V(d)} over {n}} Q^{-1}left(epsilon right)$, 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 $Q^{-1}left(cdot right)$ is the inverse of the standard Gaussian complementary cumulative distribution function. [PUBLICATION 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. |
| Author | Verdu, S. Kostina, Victoria |
| Author_xml | – sequence: 1 givenname: Victoria surname: Kostina fullname: Kostina, Victoria email: vkostina@princeton.edu organization: Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA – sequence: 2 givenname: S. surname: Verdu fullname: Verdu, S. email: verdu@princeton.edu organization: Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA |
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| SubjectTerms | Achievability Approximation Blocking Coding theory Compressing converse Dispersions Distortion Distortion measurement finite blocklength regime Frequency modulation Gaussian Inverse lossy source coding Mathematical analysis Mean square error methods memoryless sources Normal distribution Probability Rate distortion theory Rate-distortion Shannon theory Source coding Stochastic control theory |
| Title | Fixed-Length Lossy Compression in the Finite Blocklength Regime |
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