Use of a $d$-Constraint During LDPC Decoding in a Bliss Scheme

Bliss schemes of a run length limited (RLL) codec in combination with an LDPC codec, generate LDPC parity bits over a systematic sequence of RLL channel bits that are inherently redundant as they satisfy e.g. a d = 1 minimum run length constraint. That is the subsequences consisting of runs of length d = 1, viz. . . . 010 . . . and . . . 101 . . ., cannot occur. We propose to use this redundancy during LDPC decoding in a Bliss scheme by introducing additional d-constraint nodes in the factor graph used by the LDPC decoder. The messages sent from these new nodes to the variable or codeword bit nodes exert a “force” on the resulting soft-bit vector coming out of the LDPC decoding that give it a tendency to comply with the d-constraints. This way, we can significantly reduce the probability of decoding error.