An approach is provided for generating Low Density Parity Check (LDPC) codes. An LDPC encoder generates a LDPC code with an outer Bose Chaudhuri Hocquenghem (BCH) code. For 1/3 rate, the relevant parameters are as follows: q=120, n.sub.ldpc=64,800, k.sub.ldpc=n.sub.BCH=21600, k.sub.BCH=21408 (12 bit error correcting BCH). For 1/4 rate, the LDPC code has the following relevant parameters: q=135, n.sub.ldpc=64,800, k.sub.ldpc=n.sub.BCH=16200, k.sub.BCH=16008 (12 bit error correcting BCH). For rate, the following parameters exist: q=108, n.sub.ldpc=64800, k.sub.ldpc=n.sub.BCH=25920, k.sub.BCH=25728 (12 bit error correcting BCH). The above approach has particular application in digital video broadcast services over satellite.