Iterative reconstruction algorithms in compressed sensing

In this paper we give an overview of current results in iterative reconstruction of sparse signals using parity check matrices of low-density parity check (LDPC) codes as measurement matrices in compressed sensing. We provide a detailed explanation of two iterative reconstruction algorithms, Interval Passing (IP) algorithm and verification algorithm. We then compare their performance using parity check matrices of quasi-cyclic low-density parity check (QC-LDPC) codes with different column-weights and rates.