Some problems of Graph Based Codes for Belief Propagation decoding

A) , (L J regular QC-LDPC code of length N is defined by a parity-check matrix L L p I p I p I p I p I p I p I p I p I H     (1) where 1 1    J j , 1 1    L l and   l j p I , represents the p p  circulant permutation matrix obtained by cyclically right-shifting the p p  identity matrix   0 I by l j p , positions, with. / L N p  For a specific QC-LDPC code we define the corresponding " base matrix " (" mother matrix ") as the matrix of circulant shift that defines the QC-LDPC code: L L p p p p p p p p p B     (2). where  is Hadamar product For) , (L J QC-LDPC regular code mask matrix: