Iterative decoding of robust analog product codes

In this paper, a new robust analog error correcting code with an iterative decoder is proposed for real-valued signals corrupted by impulsive noises (sparse signal) in the presence of small additive noise affecting all the entries of the received signal. In each iteration of the algorithm, the problem of decoding the long block code is decoupled into a set of parallel LASSO subproblems in order to locate the impulsive errors. Then, the information is decoded by solving the appropriate least squares (LS) problem. Under the almost sparse noise model, simulation results show that the proposed algorithm exhibits little loss compared to the ideal least squares when the impulsive noises are perfectly known at the receiver.