Rényi information dimension: 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:
IEEE Transactions on Information Theory
Year:
2010

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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 or decompressor is constrained by various regularity conditions, in particular linearity of the compressor and Lipschitz continuity of the decompressor. The fundamental limit is shown to be the information dimension proposed by Rényi in 1959.