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

TL;DR

This paper introduces a method to improve LDPC decoding in Bliss schemes by incorporating $d$-constraint nodes, leveraging inherent redundancy to enforce run length constraints and reduce decoding errors.

Contribution

It proposes adding $d$-constraint nodes to the LDPC decoder's factor graph, utilizing redundancy to enhance decoding accuracy in Bliss schemes.

Findings

Significant reduction in decoding error probability

Effective enforcement of run length constraints

Improved decoding performance demonstrated

Abstract

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.