Expander codes over reals, Euclidean sections, and compressed sensing

Venkatesan Guruswami*, James R. Lee, Avi Wigderson

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Classical results from the 1970's state that w.h.p. a random subspace of N-dimensional Euclidean space of proportional (linear in N) dimension is "well-spread" in the sense that vectors in the subspace have their ℓ2 mass smoothly spread over a linear number of coordinates. Such well-spread subspaces are intimately connected to low distortion embeddings, compressed sensing matrices, and error-correction over reals. We describe a construction inspired by expander/Tanner codes that can be used to produce well-spread subspaces of Ω(N) dimension using sub-linear randomness (or in sub-exponential time). These results were presented in our paper [10]. We also discuss the connection of our subspaces to compressed sensing, and describe a near-linear time iterative recovery algorithm for compressible signals.

Original languageEnglish
Title of host publication2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Pages1231-1234
Number of pages4
DOIs
StatePublished - 2009
Externally publishedYes
Event2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States
Duration: 30 Sep 20092 Oct 2009

Publication series

Name2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

Conference

Conference2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Country/TerritoryUnited States
CityMonticello, IL
Period30/09/092/10/09

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