On the Design of Generalized LDPC Codes with Component BCJR Decoding

Generalized low-density parity-check (GLDPC) codes, where the single parity-check (SPC) nodes are replaced by generalized constraint (GC) nodes, are known to offer a reduced gap to capacity when compared with conventional LDPC codes, while also maintaining linear growth of minimum distance. However, for certain classes of practical GLDPC codes, there remains a gap to capacity even when utilizing blockwise decoding algorithm at GC nodes. In this work, we propose to optimize the design of GLDPC codes where the GC nodes are decoded with a trellis-based bit-wise Bahl-Cocke-Jelinek-Raviv (BCJR) component decoding algorithm. We analyze the asymptotic threshold behavior of GLDPC codes and determine the optimal proportion of the GC nodes in the GLDPC Tanner graph. We show significant performance improvements compared to existing designs with the same order of decoding complexity.