An encoding system includes a first low density parity check (LDPC) module and a second LDPC module. The first LDPC module is configured to generate a first encoded codeword by encoding a first codeword using a first LDPC code. The second LDPC module is configured to generate a second encoded codeword by encoding a second codeword using a second LDPC code. Signals based on the first encoded codeword and signals based on the second encoded codeword are transmitted over a communications channel. The first LDPC code is defined by a first parity check matrix and the second LDPC code is defined by a second parity check matrix. The second parity check matrix includes the first parity check matrix, a zero matrix, and a supplementary matrix.