A modified two-bit finite-alphabet iterative decoder (FAID) is proposed in this paper. As distinct from similar existing two-bit FAIDs, this proposed decoder is probabilistic and incorporates the idea of using single a-posteriori message to replace the conventional variable-to-check (v2c) messages. This brings significant variable-node unit (VNU) complexity reduction. For high-rate regular LDPC codes, it is demonstrated that the proposed decoder, in waterfall region, substantially outperforms other simplified decoders reported in the literature.

We derive a recursive algorithm to compute the joint maximum a posteriori probabilities of p consecutive bits on partial response channels. This channel detector is optimal for nonbinary soft-iterative decoding with multiple channel iterations. It is validated on a nonbinary low-density parity-check coded perpendicular magnetic recording channel.