To　decode　the　transmit　message　pairs　and　then　obtain　the　exclusive　OR　(XOR)　message,　this　letter　proposes　the　double-reliability-based　decoding　(DRB)　algorithms　with　informed　dynamic　scheduling　(IDS)　for　low-density　parity-check　(LDPC)　coded　physical-layer　network　coding　(PNC)　systems.　The　proposed　DRB　decoding　with　informed　stability　(IS-DRB)　utilizes　a　new　stability　measure　to　determine　the　update　order　of　the　check　nodes.　Moreover,　by　exploiting　the　principle　of　PNC　decoding,　we　present　an　improved　IS-DRB　(IIS-DRB)　decoding　to　select　the　check　node　with　unsatisfied　PNC　mapped　checksum　and　the　large　stability　to　update　first.　This　is　due　to　that　message　propagated　from　this　check　node　can　quickly　correct　the　variable　node　that　causes　unsatisfied　checksum.　Simulation　results　show　that　the　proposed　algorithms　can　realize　significant　performance　improvement　of　about　0.5　dB　over　the　conventional　DRB　decoding　with　the　limited　increase　in　complexity.