Check-hybrid GLDPC Codes: Systematic Elimination of Trapping Sets and Guaranteed Error Correction Capability

摘要

In this paper, we propose a new approach to construct a class of check-hybridgeneralized low-density parity-check (CH-GLDPC) codes which are free of smalltrapping sets. The approach is based on converting some selected check nodesinvolving a trapping set into super checks corresponding to a 2-errorcorrecting component code. Specifically, we follow two main purposes toconstruct the check-hybrid codes; first, based on the knowledge of the trappingsets of the global LDPC code, single parity checks are replaced by super checksto disable the trapping sets. We show that by converting specified single checknodes, denoted as critical checks, to super checks in a trapping set, theparallel bit flipping (PBF) decoder corrects the errors on a trapping set andhence eliminates the trapping set. The second purpose is to minimize the rateloss caused by replacing the super checks through finding the minimum number ofsuch critical checks. We also present an algorithm to find critical checks in atrapping set of column-weight 3 LDPC code and then provide upper bounds on theminimum number of such critical checks such that the decoder corrects all errorpatterns on elementary trapping sets. Moreover, we provide a fixed set for aclass of constructed check-hybrid codes. The guaranteed error correctioncapability of the CH-GLDPC codes is also studied. We show that a CH-GLDPC codein which each variable node is connected to 2 super checks corresponding to a2-error correcting component code corrects up to 5 errors. The results are alsoextended to column-weight 4 LDPC codes. Finally, we investigate the eliminatingof trapping sets of a column-weight 3 LDPC code using the Gallager B decodingalgorithm and generalize the results obtained for the PBF for the Gallager Bdecoding algorithm.