Adaptive sensing using deterministic partial Hadamard matrices

S. Haghighatshoar, E. Abbe, E. Telatar

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

13 Scopus citations

Abstract

This paper investigates the construction of deterministic measurement matrices preserving the entropy of a random vector with a given probability distribution. In particular, it is shown that for a random vector with i.i.d. discrete components, this is achieved by selecting a subset of rows of a Hadamard matrix such that (i) the selection is deterministic (ii) the fraction of selected rows is vanishing. In contrast, it is shown that for a random vector with i.i.d. continuous components, no entropy preserving measurement matrix allows dimensionality reduction. These results are in agreement with the results of Wu-Verdu on almost lossless analog compression and provide a low-complexity measurement matrix. The proof technique is based on a polar code martingale argument and on a new entropy power inequality for integer-valued random variables.

Original languageEnglish (US)
Title of host publication2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
Pages1842-1846
Number of pages5
DOIs
StatePublished - 2012
Event2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
Duration: Jul 1 2012Jul 6 2012

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8105

Other

Other2012 IEEE International Symposium on Information Theory, ISIT 2012
CountryUnited States
CityCambridge, MA
Period7/1/127/6/12

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Analog compression
  • Compressed sensing
  • Entropy power inequality
  • Entropy-preserving matrices

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