Abstract: In the compressed sensing theory,the Basis Pursuit BP algorithm can solve the problem of the minimum value of the l1 norm.The Primal-dual interior point method is used to reconstruct the sparse signal.For the linear block code decoding,if the error pattern E is treated as the one-dimensional sparse signal,the compressed sensing model of the reconstructing error pattern E is deduced by the compressed sensing under the no noise condition.The check matrix H is used as the measurement matrix,and the syndrome S is used as the measurement signal.The error pattern E can be reconstructed by the Basis Pursuit BP algorithm.It proves that the reconstructing error pattern E is correct.The simulation experiment of decoding the linear block code is designed.The Hamming code is decoded by the basis pursuit BP algorithm and the maximum likelihood algorithm.The BCH code is decoded by the basis pursuit BP algorithm and the Berlekamp algorithm.By the bit error rate and the code word C reconstructing success rate,the decoding performance is compared and analyzed.The simulation experiment result proves that the hamming code and the BCH code can be decoded well by the compressed sensing theory and the basis pursuit BP algorithm.