Decoding Method of the Cyclic Code Based on the Compressive Sensing Theory

By the compressive sensing theory under the no noise condition, the compressive sensing model of the reconstructing error pattern E is proposed. The syndrome S is used as the measuring signals, the check matrix H is used as the measuring matrix, the error pattern E is reconstructed by the generalized orthogonal matching pursuit gOMP algorithm and the basis pursuit BP algorithm, then the value of the code word C is estimated. Taking the (9,3) cyclic code as example, it proves that the reconstructing error pattern E is correct. Taking the (7,1),(7,3), (7, 4), (9, 3) and (15,9) cyclic code as example, it proves that the correcting error capability of the cyclic code is correct. The simulation experiment of the cyclic code is designed, taking the (7,3),(9,3) and (15,11) cyclic code as example, the simulation experiment is completed. By the bit error rate and the success rate of the reconstructing code word C, the decoding effect of the gOMP algorithm and the basis pursuit BP algorithm and the maximum likelihood algorithm is analyzed and compared. The experiment result show that the cyclic code can be decoded well by the the gOMP algorithm and the BP algorithm based on the compressive sensing theory.