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