An Efficient Algorithm to Improve the Success Threshold of Node-Based Verification-Based Algorithms in Compressed Sensing

In this letter, we introduce an algorithm to enhance the success threshold of node-based verification-based (NB-VB) algorithms in compressed sensing. The NB-VB algorithms have low computational complexity, and are generally classified as iterative message passing algorithms employed for signal recovery. However, similar to the standard iterative decoding of low-density parity-check codes over the binary erasure channel (BEC) in the context of channel coding, these algorithms become inefficient in the stopping sets. The proposed method, with the inspiration of improved decoding algorithms over the BEC, enhances the performance of NB-VB algorithms by guessing values of some unverified signal elements. Our simulation results indicate that although the proposed method improves the success threshold significantly, it does not cause any considerable increase in the complexity of standard NB-VB algorithms.