Abstract: Applying the compressive sensing theory to the decoding of the linear block code, we proposed the compressive sensing model of the reconstructing the error pattern [WTHX]E[WT], the check matrix [WTHX]H[WT] as the form and properties of the measurement matrix. The syndrome [WTHX]S[WT] was used as the measurement signal, the check matrix [WTHX]H[WT] was used as the measurement matrix, and the cyclic code (15,7) was used as the example to reconstruct the estimation of the error pattern [WTHX]E[WT] by using the basis pursuit (BP) algorithm. The simulation experiment scheme of the decoding of the linear block code was designed. The simulation experiment results show that the linear block codes can be decoded well by the compressive sensing theory and the BP algorithm.

Key words: compressive sensing (CS)； basis pursuit (BP) algorithm； cyclic code； BCH code； Hamming code； check matrix； syndrome, error pattern