Generally, a 7/8 rate LDPC parity check matrix H_n, with a codeword length of either 672 or 1344, may be generated from the rate 13/16 LDPC parity check matrix H, by selecting and adding any two rows of partitioned submatrices of the rate 13/16 LDPC parity check matrix H as the first row of the new 7/8 rate LDPC parity check matrix H_n, and using the remaining one row as the second row of the new 7/8 rate LDPC parity check matrix H_n. If the codeword length is 672, Z=42; if the codeword length is 1344, Z=84.

As well, a 7/8 rate LDPC parity check matrix H_n, with a codeword length of either 672 or 1344, may be generated from the rate 3/4 LDPC parity check matrix H, by selecting and adding any two or more rows of partitioned submatrices of the rate 3/4 LDPC parity check matrix H as the first row of the new 7/8 rate LDPC parity check matrix H_n, and by adding the remaining one or more rows as the second row of the new 7/8 rate LDPC parity check matrix H_n. If the codeword length is 672, Z=42; if the codeword length is 1344, Z=84.

Similarly, a 7/8 rate LDPC parity check matrix H_n, with a codeword length of either 672 or 1344, may be generated from the rate 1/2 or 5/8 LDPC parity check matrix H, by adding any two or more rows of partitioned submatrices of the rate 1/2 or 5/8 LDPC parity check matrix H as the first row of the new 7/8 rate LDPC parity check matrix H_n, and then adding the remaining rows as the second row of the new 7/8 rate LDPC parity check matrix H_n. If the codeword length is 672, Z=42, if the codeword length is 1344, Z=84.

Codeword Length=1344, Z=42