@inproceedings{d40df1a5b3234c0e81a0483aee7bb248,

title = "Fixed-length lossy compression in the finite blocklength regime: Gaussian source",

abstract = "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).",

keywords = "Gaussian source, Shannon theory, achievability, converse, finite blocklength regime, lossy source coding, memoryless sources, rate distortion, sphere covering",

author = "Victoria Kostina and Sergio Verd{\'u}",

year = "2011",

doi = "10.1109/ITW.2011.6089501",

language = "English (US)",

isbn = "9781457704376",

series = "2011 IEEE Information Theory Workshop, ITW 2011",

pages = "457--461",

booktitle = "2011 IEEE Information Theory Workshop, ITW 2011",

note = "2011 IEEE Information Theory Workshop, ITW 2011 ; Conference date: 16-10-2011 Through 20-10-2011",

}