TY - GEN

T1 - The dispersion of lossy source coding

AU - Ingber, Amir

AU - Kochman, Yuval

PY - 2011

Y1 - 2011

N2 - In this work we investigate the behavior of the minimal rate needed in order to guarantee a given probability that the distortion exceeds a prescribed threshold, at some fixed finite quantization block length. We show that the excess coding rate above the rate-distortion function is inversely proportional (to the first order) to the square root of the block length. We give an explicit expression for the proportion constant, which is given by the inverse Q-function of the allowed excess distortion probability, times the square root of a constant, termed the excess distortion dispersion. This result is the dual of a corresponding channel coding result, where the dispersion above is the dual of the channel dispersion. The work treats discrete memoryless sources, as well as the quadratic-Gaussian case.

AB - In this work we investigate the behavior of the minimal rate needed in order to guarantee a given probability that the distortion exceeds a prescribed threshold, at some fixed finite quantization block length. We show that the excess coding rate above the rate-distortion function is inversely proportional (to the first order) to the square root of the block length. We give an explicit expression for the proportion constant, which is given by the inverse Q-function of the allowed excess distortion probability, times the square root of a constant, termed the excess distortion dispersion. This result is the dual of a corresponding channel coding result, where the dispersion above is the dual of the channel dispersion. The work treats discrete memoryless sources, as well as the quadratic-Gaussian case.

KW - Central limit theorem

KW - Dispersion

KW - Excess distortion exponent

KW - Rate disortion

UR - http://www.scopus.com/inward/record.url?scp=79955707785&partnerID=8YFLogxK

U2 - 10.1109/DCC.2011.13

DO - 10.1109/DCC.2011.13

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AN - SCOPUS:79955707785

SN - 9780769543529

T3 - Data Compression Conference Proceedings

SP - 53

EP - 62

BT - Proceedings - DCC 2011

T2 - 2011 Data Compression Conference, DCC 2011

Y2 - 29 March 2011 through 31 March 2011

ER -