… block-circulant parity check matrix structure enables … Parity check matrix of a QC-LDPC
code is a grid of submatrices, which are either circulant permutation matrices or all-zero matrices. …

… permutations, one can put such a paritycheck matrix in the form of a diagonal array of matrices…
n0 array, H, of e × e circulant permutation matrices from the base matrix defined as follows: …

… circulant permutation matrix (CPM) whose top row is given by the … We presented combinatorial
expressions for the ranks of the parity check matrices of QC-LDPC codes on Latin squares…

… As a comparison, in [7, Example 3], a (4, 32)-regular (4608, 4033) quasi cyclic LDPC code,
whose construction is based on circulant permutation matrices, is proposed for burst erasure …

… -density-parity-check codes, exempt of cycle of length 4, based on a circulant permutation
matrix, … structure is applied to guarantee that parity check bits can be recursively computed with …

… parity-check polynomial matrix from A and provide a concise and intrinsic proof based on
the properties of cyclic codes and a lemma for circulant matrices and polynomial residue rings. …

… The first approach is to design (or transform) sparse parity-check matrices such that they
have approximate triangular form (such possible transformations rely only on permutations of …

… In symbol representation, these parity-check matrices are of size L × N, where L = JM and
N = KM. We assume that the permutation matrices Pjk of the parity-check matrices H are cho…

… The design is carried out by an ad hoc search algorithm over the column permutations of
the parity-check matrix. Our simulations show that the proposed reliability-based coded …

… parity check matrix can be constructed using patterned sub-matrix structure such that the
matrix … all zero matrix (Z), an identity matrix (I), permutation matrices (PM1 and PM2) of identity …