Methods for the Soft-Decision Decoding of MTR Codes in Multiple-Head Magnetic Recording Systems

Two different methods for the soft-decision decoding of the maximum-transition-run (MTR) codes have been considered in this paper. The first one, the maximum a posteriori (MAP) algorithm, is based on the Bayesian algorithm, computing a posteriori log-likelihood ratios (LLR) using MTR codewords. The second one, the soft-decision implementation in Boolean logic circuits has been used to propagate the soft-values through the MTR decoder. The MTR code performs as an inner encoding code, in a simple concatenation of the low-density parity-check (LDPC) and the MTR. The special case of two-track two-head E2PR4 channel model was used, assuming the low level of inter-track interference (ITI) and the AWGN noise presence. The soft-decision decoding results with nearly 1.7dB coding gain, using the MAP algorithm, while nearly 1.9dB, using the second one approach.