Design of high-rate irregular non-binary LDPC codes using algorithmic stopping-set cancellation

Following Poulliat et al.´s design of (2, d_c) nonbinary LDPC (NB-LDPC) codes, this paper designs high-rate irregular NB-LDPC codes by addressing the problem of minimum symbol distance. The design procedure first identifies all stopping sets up to weight five in an LDPC code and enumerates them via a message passing algorithm. For each identified stopping set, careful labeling forces its corresponding parity-check sub-matrix to be full rank, thereby preventing the stopping set from being a sub-code and ensuring a minimum distance of at least six symbols. Simulation results for codes designed through this procedure show a significant improvement in the error-floor region over randomized labeling.