Local recovery in data compression for general sources

Arya Mazumdar, Venkat Chandar, Gregory W. Wornell

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

Source coding is concerned with optimally compressing data, so that it can be reconstructed up to a specified distortion from its compressed representation. Usually, in fixed-length compression, a sequence of n symbols (from some alphabet) is encoded to a sequence of k symbols (bits). The decoder produces an estimate of the original sequence of n symbols from the encoded bits. The rate-distortion function characterizes the optimal possible rate of compression allowing a given distortion in reconstruction as n grows. This function depends on the source probability distribution. In a locally recoverable decoding, to reconstruct a single symbol, only a few compressed bits are accessed. In this paper we find the limits of local recovery for rates near the rate-distortion function. For a wide set of source distributions, we show that, it is possible to compress within ϵ of the rate-distortion function such the local recoverability grows as Ω(log(1/ϵ)); that is, in order to recover one source symbol, at least Ω(log(1/ϵ)) bits of the compressed symbols are queried. We also show order optimal impossibility results. Similar results are provided for lossless source coding as well.

Original languageEnglish (US)
Title of host publicationProceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2984-2988
Number of pages5
ISBN (Electronic)9781467377041
DOIs
StatePublished - Sep 28 2015
EventIEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong
Duration: Jun 14 2015Jun 19 2015

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2015-June
ISSN (Print)2157-8095

Other

OtherIEEE International Symposium on Information Theory, ISIT 2015
CountryHong Kong
CityHong Kong
Period6/14/156/19/15

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    Mazumdar, A., Chandar, V., & Wornell, G. W. (2015). Local recovery in data compression for general sources. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 (pp. 2984-2988). [7283004] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2015.7283004