Constrained coding and detection for TDMR using generalized belief propagation

In this paper, we propose two-dimensional (2D) constraints for mitigating media noise in two-dimensional magnetic recording (TDMR) systems with generalized belief propagation (GBP) detectors. By imposing restrictions on 2D input patterns, we forbid patterns harmful to the GBP detector. Such 2D constraints result in an order of magnitude improvement in the bit error rate. This improvement is demonstrated on TDMR systems with realistic grain, bit, track and head dimensions. We also estimate the capacities of locally defined 1D and 2D low-pass constraints using the GBP-based method.