Support recovery with sparsely sampled free random matrices

Antonia Tulino, Giuseppe Caire, Shlomo Shamai, Sergio Verdu

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

13 Scopus citations

Abstract

Consider a Bernoulli-Gaussian complex n-vector whose components are X iBi, with Bi ∼Bernoulli-q and Xi ∼CN(0; σ2), iid across i and mutually independent. This random q-sparse vector is multiplied by a random matrix U, and a randomly chosen subset of the components of average size np, p ∈[0; 1], of the resulting vector is then observed in additive Gaussian noise. We extend the scope of conventional noisy compressive sampling models where U is typically the identity or a matrix with iid components, to allow U that satisfies a certain freeness condition, which encompasses Haar matrices and other unitarily invariant matrices. We use the replica method and the decoupling principle of Guo and Verdú, as well as a number of information theoretic bounds, to study the input-output mutual information and the support recovery error rate as n→∞.

Original languageEnglish (US)
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages2328-2332
Number of pages5
DOIs
StatePublished - Oct 26 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: Jul 31 2011Aug 5 2011

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8104

Other

Other2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
CountryRussian Federation
CitySt. Petersburg
Period7/31/118/5/11

All Science Journal Classification (ASJC) codes

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

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