Reverse concatenation for product codes

A reverse concatenation encoding system for a recording write path, comprising:

• a user data array generator operable to process input user data and generate a first data array;
• a first modulation encoder operable to impose a first modulation constraint on a respective row of the first data array and generate a second data array comprising modulation-constrained data;
• a formatter operable to process the second data array by inserting predetermined empty locations in each column of the second data array interleaved with the modulation-constrained data and generate a third data array;
• a C2-encoder operable to compute a C2-parity byte for each of a plurality of the empty locations in each column of the third data array and generate a fourth data array;
• a C1-encoder operable to compute a C1-parity symbol for each row of the fourth data array and generate a fifth data array;
• a second modulation encoder operable to impose a second modulation constraint on each C1-parity symbol of the fifth data array and generate a sixth data array;
• and
• means for recording the rows of the sixth data array onto tracks of a recording medium.