Local recovery in data compression for general sources

Arya Mazumdar; Venkat Chandar; Gregory W. Wornell

doi:10.1109/ISIT.2015.7283004

Local recovery in data compression for general sources

Arya Mazumdar
, Venkat Chandar
, Gregory W. Wornell

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

19 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 language	English (US)
Title of host publication	Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2984-2988
Number of pages	5
ISBN (Electronic)	9781467377041
DOIs	https://doi.org/10.1109/ISIT.2015.7283004
State	Published - Sep 28 2015
Externally published	Yes
Event	IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong Duration: Jun 14 2015 → Jun 19 2015

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2015-June
ISSN (Print)	2157-8095

Other

Other	IEEE International Symposium on Information Theory, ISIT 2015
Country/Territory	Hong Kong
City	Hong Kong
Period	6/14/15 → 6/19/15

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Publisher link

10.1109/ISIT.2015.7283004

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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). Article 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

Local recovery in data compression for general sources. / Mazumdar, Arya; Chandar, Venkat; Wornell, Gregory W.
Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2984-2988 7283004 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Mazumdar, A, Chandar, V & Wornell, GW 2015, Local recovery in data compression for general sources. in Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015., 7283004, IEEE International Symposium on Information Theory - Proceedings, vol. 2015-June, Institute of Electrical and Electronics Engineers Inc., pp. 2984-2988, IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, Hong Kong, 6/14/15. https://doi.org/10.1109/ISIT.2015.7283004

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AB - 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.

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Local recovery in data compression for general sources

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