Codes satisfying maximum transition run and parity-check constraints

Efficient combination of a modulation code with a parity-check code is studied for magnetic recording systems. A new approach to the design of combined modulation/parity codes that largely retains the properties of the original modulation code is proposed. It is based on the matrix transformation of a set of desired parity-check equations at the partial-response channel input into a set of parity-check equations at the input of the precoder. The code design methodology is illustrated by constructing a rate-96/104 dual-parity code that satisfies maximum transition run constraints. Simulation results for a Lorentzian recording channel show that this code significantly outperforms a single-parity code for channels dominated by electronics noise. Moreover, the rate-96/104 dual-parity code, which has been used extensively in commercial disk drives, performs as well as a single-parity code in stationary/nonstationary data-dependent noise conditions. Finally, the low-average-transition-density constraint is proposed to enhance error-rate performance in channels dominated by transition noise.