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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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 58; no. 6; pp. 3309 - 3338
Main Authors: Kostina, Victoria, Verdu, S.
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2012
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary: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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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2012.2186786