Based on LDPC parity check matrix generated by the LDPC matrix generator 302, the generator matrix module 304 may generate a generator matrix G. The generator matrix G in systematic form which is correspondent to H can be G=[IkPT], where “T” denotes the matrix transpose. The generator matrix G is a binary K×N matrix. The row space of G is orthogonal to H such that GHT=0. Therefore, in LDPC encoding, once H has been designed, G can also be determined accordingly. As well, the matrix H satisfies H
The source word input interface 306 receives the source words from the source words segmenting module 202. As discussed previously, the received source word may be considered as a row vector ū[u1, . . . , uK]. The source word input interface 306 is then forward the received source words to the codewords generator 308. With the source word ū=[u1, . . . , uk] and the binary (K×N) generator matrix G, by multiplying the source word with the generator matrix G, ū·G=