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Provided is a base matrix of a rate-adaptive irregular QC-LDPC code, the base matrix being formed by columns and rows having entries representing circulant submatrices. The columns of the base matrix are divided into at least one or more higher weight first columns and lower weight second columns and the rows of the base matrix are divided into first high weight rows corresponding to the high rate mother code and second low weight rows corresponding to the extension part related to lower rate codes. A first submatrix formed by an intersection of entries of the second columns and entries of the first and the second rows is divided into first quadratic submatrices, wherein at most one entry in each column of each first submatrix and/or at most one entry in each row of each first submatrix is labelled thereby dividing the first submatrix into layers of groups of orthogonally labelled rows, wherein the number of orthogonally labelled rows corresponds to the size of the first quadratic submatrices. One or more check node unit processors perform flooding or a combination of flooding and layered (hence hybrid) decoding operations in view of the one or more higher weight first columns and one or more CNU processors perform layered decoding operations in view of the second columns.