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We propose a verification-based algorithm for noiseless Compressed Sensing that reconstructs the original signal operating on a sparse graph. The proposed scheme has affordable computational complexity and its performance is significantly better than previous verification-based algorithms and similar to AMP-based algorithms. We also show that the performance of a noiseless compressed sensing scheme when verification-based algorithms and a sparse matrix is employed to reconstruct the original signal can be upper bounded by the performance of a LDPC code employing the same parity matrix when correcting a codeword transmitted through a BEC.
CitationRamirez, F., Lamarca, M. List message passing algorithm for noiseless compressed sensing. A: Asia-Pacific Signal and Information Processing Association Annual Summit and Conference. "Proceedings of APSIPA Annual Summit and Conference 2015". Hong-Kong: 2015, p. 1116-1120.
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