Combined modulation/parity codes for magnetic recording

Inner coding schemes for magnetic recording that cascade a modulation encoder with a parity-check encoder followed by a precoder are considered. A set of desired parity-check equations that are satisfied by the combined modulation/parity code words at the output of the precoder is transformed into a set of parity-check equations at the input of the precoder. Efficient combination of a maximum transition run (MTR) code with a parity-check code is demonstrated by constructing a rate-96/104 combined MTR/parity code that largely retains the properties of the original MTR code.