PurposeThe purpose of this paper is to research the traditional belief‐propagation (BP) decoding algorithm of low‐density parity‐check code. The big computation load is a shortcoming of traditional BP decoding algorithm. Accordingly, the paper provides an improved BP decoding algorithm which raises the decoding efficiency and reduces decoding time delay.Design/methodology/approachAn improved BP decoding algorithm is studied and the error correction performance of the improved BP decoding algorithm in the Gaussian channel is provided.FindingsThe simulation result shows the improved BP decoding algorithm has lower computational complexity and higher decoding speed based on the premise of a little decoding performance loss.Research limitations/implicationsThe improved BP decoding algorithm has lower computational complexity and higher decoding speed based on the premise of a little decoding performance loss.Practical implicationsThe improved BP decoding algorithm raises the decoding efficiency and reduces decoding time delay.Originality/valueThe decoding algorithm only needs to update the wrong bit information which might arise, but not update the bit information whose reliability is very high. The improved BP decoding algorithm raises the decoding efficiency and reduces decoding time delay.

In this paper, an efficient high-order multiple signal classification (MUSIC)-like method is proposed for mixed-field source localization. Firstly, a non-Hermitian matrix is designed based on a high-order cumulant. One of the steering matrices, that is related only with the directions of arrival (DOA), is proved to be orthogonal with the eigenvectors corresponding to the zero eigenvalues. The other steering matrix that contains the information of both the DOA and range is proved to span the same column subspace with the eigenvectors corresponding to the non-zero eigenvalues. By applying the Gram–Schmidt orthogonalization, the range estimation can be achieved one by one after substituting each estimated DOA. The analysis shows that the computational complexity of the proposed method is lower than other methods, and the effectiveness of the proposed method is shown with some simulation results.