An LDPC parity check matrix, includes a systematic portion having a plurality of systematic elements having a value, the value each systematic element determining a cyclic shift to be applied to rows of an identity submatrix corresponding to that element; and a parity portion having a plurality of panty elements having a value, the value of each parity element determining a cyclic shift to be applied to rows of an identity submatrix corresponding to that element; wherein the weights of each column of a group of columns of the parity portion is the same. The LDPC parity check matrix may be used for data access, communication and storage, and may be used, for example for communications among a plurality of network nodes.