List message passing algorithm for noiseless compressed sensing

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.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.Peer ReviewedPostprint (published version

List message passing algorithm for noiseless compressed sensing

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.Peer Reviewe