According to one embodiment of the present disclosure, there is provided a method for encoding a source word. The method comprises receiving a 1×K source word row vector ū; and generating a 1×N codeword vector c=ū·G, wherein G is a K×N generator matrix, and wherein G is derived from a parity check matrix H_n, and H_n having a lifting factor Z, and wherein the H_n comprises a plurality of submatrices, each submatrix having a size Z×Z, and wherein at least one submatrix has m₁ diagonals of “1”, and wherein m₁. is an integer>=2.

According to one embodiment of the present disclosure, G=[I_kP^T], where P_(n?k)×k is a binary matrix and I_(n?k) is the identify matrix of order n?k, where “T” denotes the matrix transpose; and wherein a parity check matrix Hn=[P_(n?k)×kI_(n?k)].

According to one embodiment of the present disclosure, H_n is generated by partitioning a first M×N parity check matrix H, with a lifting factor of Z, wherein M=I×Z, N=J×Z, and wherein I and J are integers, I>2 and J>0, into square submatrices, wherein the partitioned parity check matrix H contains submatrices of (M/Z) rows×(N/Z) columns; selecting m₁ rows from the M/Z rows of submatrices of the partitioned parity check matrix H; and adding the m₁ rows of the submatrices of the first partitioned parity check matrix H as a row of submatrices of the matrix H_n, and m₁ is a integer>=2. In one embodiment, M?(m₁×Z)+Z=N?K. In one embodiment, Z=42, N=672. In another embodiment, K=588, and the new matrix H_n, comprises 84 rows×672 columns.