Verification-based algorithm for compressed sensing using GLDPC codes

In this paper, we present a new family of sparse measurement matrices and low complexity reconstruction algorithm in compressed sensing (CS). Our CS system is designed from the generalized low-density parity check code (GLDPC), and to reconstruct the signal by using a simple verification-based (VB) algorithm. In particular, our scheme also can cope with the case of noisy measurements, comparing with most work about VB algorithm is designed in noiseless case. Furthermore, we present the density evolution techniques for the analysis of the VB algorithm in the asymptotic dimension. The analysis can predict the percentage of unrecovered signal coefficients over the ensembles of input signal and measurement matrix. Simulation results are also given, which reveal that the theoretical results match that of the reconstruction algorithm and it is superior to the existing algorithms.