The Min-Max in LC and Max-Log MAP in LC for MTR Decoding in Two-Track Magnetic Recording Systems

The soft-decision decoding methods for maximum-transition-run (MTR) codes have been considered extensively, in order to enable a wider implementation of MTR codes in magnetic recording systems. The approaches, named as the min-max in LC and the max-log MAP in LC have been proposed, emerging as reasonable solutions for MTR codes. Both methods force the soft-values propagation through the Boolean logic circuits of decoder, encouraging the concatenation of MTR with some powerful error-correcting codes, such as low-density parity-check (LDPC) codes. In this paper, the min-max in LC and the max-log MAP in LC have been analyzed in the framework of a simple LDPC-MTR concatenation, over the two-track two-head interfering E2PR4 magnetic recording channel. In the case of a rate 4/5 (2, k = 8) MTR code utilization and the low-level of inter-track interference, the proposed methods offer 1.9 dB and 1.7 dB of decoding gain, for BER = 10-5. However, the complexity analysis shows that the min-max in LC is in advantage comparing to the max-log MAP in LC.