Use of Low-Density Parity-Check Codes for Dominant Error Events Detection and $k$-Constraint Enforcement

In this paper, we propose to leverage the simple and explicit parity checks inherent in low-density parity-check (LDPC) codes to detect dominant error events without code rate penalty. This is enabled by enforcing a very weak constraint on the LDPC code parity check matrix structure. Such a constraint can be readily satisfied by most structured LDPC codes reported in the open literature, such as quasi-cyclic (QC) LDPC codes. Moreover, this zero-redundancy dominant error events detection can be extended to handle the bit errors that occur when deliberate bit-flipping is used to enforce -constraints. We have demonstrated the effectiveness of the proposed method in computer simulations.