Aconstructionmethodbasedonthep-planetodesignhigh-girthquasi-cycliclow-densityparity-check(QC-LDPC)codesisproposed.Firstlythegoodpointsineverylineofthep-planecanbeascertainedthroughfilteringthebadpoints,becausethedesignedparity-checkmatrixesusingthesepointshavetheshortcyclesinTannergraphofcodes.Thenoneofthebestpointsfromtheresidualgoodpointsofeverylineinthep-planewillbefound,respectively.Theoptimalpointisalsosingledoutaccordingtothebiterrorrate(BER)performanceoftheQC-LDPCcodesatlast.ExplicitnecessaryandsufficientconditionsfortheQC-LDPCcodestohavenoshortcyclesarepresentedwhichareinfavorofremovingthebadpointsinthep-plane.Sincepreventingtheshortcyclesalsopreventsthesmallstoppingsets,theproposedconstructionmethodalsoleadstoQC-LDPCcodeswithahigherstoppingdistance.
