Check-hybrid GLDPC Codes: Systematic Elimination of Trapping Sets and Guaranteed Error Correction Capability
Vida Ravanmehr, Mehrdad Khatami, David Declercq, Bane Vasic

TL;DR
This paper introduces check-hybrid GLDPC codes that eliminate small trapping sets by converting certain check nodes into super checks, enhancing error correction capabilities and reducing trapping set errors.
Contribution
The paper presents a novel method to construct check-hybrid GLDPC codes by converting critical checks into super checks, improving error correction and trapping set elimination.
Findings
Eliminates small trapping sets in LDPC codes
Guarantees correction of up to 5 errors with specific code constructions
Provides algorithms for identifying critical checks
Abstract
In this paper, we propose a new approach to construct a class of check-hybrid generalized low-density parity-check (CH-GLDPC) codes which are free of small trapping sets. The approach is based on converting some selected check nodes involving a trapping set into super checks corresponding to a 2-error correcting component code. Specifically, we follow two main purposes to construct the check-hybrid codes; first, based on the knowledge of the trapping sets of the global LDPC code, single parity checks are replaced by super checks to disable the trapping sets. We show that by converting specified single check nodes, denoted as critical checks, to super checks in a trapping set, the parallel bit flipping (PBF) decoder corrects the errors on a trapping set and hence eliminates the trapping set. The second purpose is to minimize the rate loss caused by replacing the super checks through…
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