The LDPC Code Based On Protograph And Its Application

The Low-Density Parity-Check(LDPC)Code has lower linear decoding complexity and is a good code with excellent performance.Therefore,the LDPC code has great research value.In recent years,the compressed sensing and the Pooling design are widely used in the field of information,and thus have been recognized in the practical application.In this paper,the protograph is constructed by using the vector space on the finite field as a theoretical tool,and then the LDPC code is constructed based on the protograph by using the modified progressive edge growth algorithm.It is applied to the research of the compressed sensing and the Pooling design.The paper combines the related content of the LDPC code,the compressed sensing theory and the Pooling design.The following works have been carried out:1.The protograph is constructed based on the inclusion relation of the subspace in the vector space over the finite field,then the LDPC codes with large girth are constructed based on the protograph by using the modified progressive edge growth algorithm.The length,code rate and number of LDPC codes are determined by using the Anzahl theorem of vector space.The constructed LDPC codes are compared with previous LDPC codes,thus getting good results.2.The LDPC code check matrix is used as the compressed sensing matrix,the coherence of the matrix is analyzed,and the orthogonal matching pursuit algorithm is used to reconstruct the one-dimensional signal and the two-dimensional image.The reconstruction effect is compared with that of previous sensing matrices,and good results are obtained.3.The protograph has been improved which is applied to the Pooling design,d~z-disjunct matrix is constructed,parameters of the matrix and the text efficiency are calculated,the low of the text efficiency with the parameter is analyzed,and comparing it with the text efficiency of previous Pooling designs.Thus good results are obtained.