Fundamental limits of almost lossless analog compression

Authors:
Yihong Wu;Sergio Verdú
Affiliations:
Department of Electrical Engineering, Princeton University, Princeton, NJ;Department of Electrical Engineering, Princeton University, Princeton, NJ
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Year:
2009

Citing 3
Cited 1

Rényi information dimension: fundamental limits of almost lossless analog compression

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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

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Compressed sensing

IEEE Transactions on Information Theory

Rényi information dimension: fundamental limits of almost lossless analog compression

IEEE Transactions on Information Theory

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Abstract

In Shannon theory, lossless source coding deals with the optimal compression of discrete sources. Compressed sensing is a lossless coding strategy for analog sources by means of multiplication by real-valued matrices. In this paper we study almost lossless analog compression for analog memoryless sources in an information-theoretic framework, in which the compressor is not constrained to linear transformations but it satisfies various regularity conditions such as Lipschitz continuity. The fundamental limit is shown to be the information dimension proposed by Rényi in 1959.