For　two-way　relay　channel-coded　physical　network　coding　(CPNC)　systems　with　sufficiently　low　code　rate,　the　separate　complete　decoding　(SCD)　scheme　outperforms　the　joint　channel-physical　network　coding　(JCNC)　scheme.　Hence,　this　paper　addresses　the　design　of　protograph　LDPC　codes　to　approach　the　SCD-based　CPNC　capacity.　In　fact,　due　to　virtual　erasures　induced　by　CPNC　transmission,　the　conventional　protograph　that　approaches　point　to　point　(P2P)　AWGN　capacity　may　not　perform　well　in　SCD-based　CPNC　channel　in　terms　of　error　rates.　We　then　use　the　finite-length　EXIT　chart　to　calculate　iterative　decoding　threshold　of　a　joint　code　graph　formed　by　two　codes　in　the　SCD.　Furthermore,　we　investigate　the　serial　separate　complete　decoding　(S-SCD)　and　parallel　separate　decoding　(P-SCD).　Simulation　results　show　that　with　the　S-SCD,　the　proposed　protograph　codes　have　within　0.9　dB　of　their　capacity　limits　for　rates　from　1/3　to　3/5.　©　2016　IEEE.