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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Chilappagari, S.K. Chertkov, M. Vasic, B. |
| Copyright Year | 2010 |
| Description | Author affiliation: Theoretical Divison & CNLS, LANL & New Mexico Consortium, Los Alamos, 87545(4), USA (Chertkov, M.) || Marvell Semiconductor Inc., Santa Clara, CA 95054, USA (Chilappagari, S.K.) || Dept. of ECE, University of Arizona, Tucson, 85721, USA (Vasic, B.) |
| Abstract | We consider the Linear Programming (LP) solution of the Compressed Sensing (CS) problem over reals, also known as the Basis Pursuit (BasP) algorithm. The BasP allows interpretation as a channel-coding problem, and it guarantees error-free reconstruction with a properly chosen measurement matrix and sufficiently sparse error vectors. In this manuscript, we examine how the BasP performs on a given measurement matrix and develop an algorithm to discover the sparsest vectors for which the BasP fails. The resulting algorithm is a generalization of our previous results on finding the most probable error-patterns degrading performance of a finite size Low-Density Parity-Check (LDPC) code in the error-floor regime. The BasP fails when its output is different from the actual error-pattern. We design a CS-Instanton Search Algorithm (ISA) generating a sparse vector, called a CS-instanton, such that the BasP fails on the CS-instanton, while the BasP recovery is successful for any modification of the CS-instanton replacing a nonzero element by zero. We also prove that, given a sufficiently dense random input for the error-vector, the CS-ISA converges to an instanton in a small finite number of steps. The performance of the CSISA is illustrated on a randomly generated 120 × 512 matrix. For this example, the CS-ISA outputs the shortest instanton (error vector) pattern of length 11. |
| Starting Page | 1978 |
| Ending Page | 1982 |
| File Size | 226696 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781424478903 |
| e-ISBN | 9781424478927 |
| e-ISBN | 9781424478910 |
| DOI | 10.1109/ISIT.2010.5513360 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2010-06-13 |
| Publisher Place | USA |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Compressed sensing Channel coding Sparse matrices Parity check codes Linear programming Pursuit algorithms Vectors Performance evaluation Degradation Algorithm design and analysis |
| Content Type | Text |
| Resource Type | Article |
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