Methods and devices are disclosed for encoding source words and decoding codewords with LDPC matrices, comprising: 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 derived from a parity check matrix Hl; and wherein Hl is derived from a base parity check matrix H by summing different rows in the base parity check matrix H to obtain an intermediate parity check matrix, and applying a lifting matrix to the intermediate base parity check matrix to obtain Hl.