TY - GEN

T1 - Fixed-length lossy compression in the finite blocklength regime

T2 - 2011 IEEE Information Theory Workshop, ITW 2011

AU - Kostina, Victoria

AU - Verdu, Sergio

PY - 2011/12/21

Y1 - 2011/12/21

N2 - For an i.i.d. Gaussian source with variance σ 2, we show that it is necessary to spend 1/2 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).

AB - For an i.i.d. Gaussian source with variance σ 2, we show that it is necessary to spend 1/2 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).

UR - http://www.scopus.com/inward/record.url?scp=83655164949&partnerID=8YFLogxK

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U2 - 10.1109/ITW.2011.6089501

DO - 10.1109/ITW.2011.6089501

M3 - Conference contribution

AN - SCOPUS:83655164949

SN - 9781457704376

T3 - 2011 IEEE Information Theory Workshop, ITW 2011

SP - 457

EP - 461

BT - 2011 IEEE Information Theory Workshop, ITW 2011

Y2 - 16 October 2011 through 20 October 2011

ER -