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.
Abstract-. We propose a novel scheme for source coding of non-uniform memoryless binary sources based on progressively encoding the input sequence with non-linear encoders. At each stage, a number of source bits is perfectly recovered, and these bits are thus not encoded in the next stage. The last stage consists of an LDPC code acting as a source encoder over the bits that have not been recovered in the previous stages.
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