| Channel coding is an important guarantee for the reliability of information transmission on noisy channels.In the new generation of mobile communications,Low-Density Parity-Check(LDPC)is used as a data channel coding scheme in the enhanced mobile broadband scenario.Its coding is simple,flexible,and easy to implement.However,in the decoding process,the iterative calculation process converges slowly at long code words.To solve this problem,this article aims to improve the decoding complexity and reduce the decoding delay by applying Compressed Sensing(CS).First,the feasibility of theoretical application is demonstrated by combining application scenarios and research contents.The mathematical description of the compressed sensing theory is given,and the main problems solved by the compressed sensing theory are pointed out.In the problem,the measurement matrix is associated with the check matrix in linear decoding.Then the standard and mathematical description of the evaluation measurement matrix are given.The theoretical connection between the linear decoding problem in sparse space and the compressive sensing recovery problem;then,prove the one-way problem: the sparse check matrix can be used as the compressive sensing measurement matrix.Then,based on the LDPC code check matrix construction method,a compressed sensing measurement matrix is designed.In the construction of graph-based measurement matrices,the matrices constructed based on the existing PEG algorithm do not have a certain structure and regularity.It needs to consume more space and computing power during storage and iteration.A grouping progressive edge generation algorithm is proposed.The matrix is given certain structural laws while maintaining random characteristics.In the construction of an algebra-based measurement matrix,the basic check matrix in the mobile broadband wireless access standard is used to expand in a finite domain.While satisfying the properties of the measurement matrix,the original check relationship is retained.Finally,the singular value decomposition is used to insensitive to matrix disturbances,and the constructed measurement matrix is further optimized.The superiority of the constructed measurement matrix is verified by simulation comparison with the existing measurement matrix.Then,combined with the above research results,this paper proposes a compressed sensing-based LDPC code decoding method and its improved method.Among them,CS theory assists the decoding structure,and uses noise as a sparse signal to calculate the error pattern.Compressed sensing direct decoding structure,combined with the measurement matrix constructed based on LDPC,gives the mathematical equations of the receiving end and the transmitting end.Constraints to achieve effective sampling,combined with reconstruction algorithms,directly restore the original signal.Compared with the existing classical decoding algorithms,the performance of the proposed method is demonstrated.Finally,the reconstruction algorithm is optimized based on sparse Bayesian learning.The LP(0 <P< 1)norm minimization method is used instead of the L1 norm minimization solution.Compared with the L1 norm,the LP norm is closer to the L0 norm,and there are more relaxed relaxation conditions and fewer measurements in the reconstruction process.In a series of literatures and related experiments,it has been proved that the LP norm minimization algorithm can achieve better performance than the convex optimization algorithm under the L1 norm. |
