In　this　letter,　we　propose　majority-logic　decoding　(MLGD)　algorithms　of　low　complexity　for　low-density　parity-check　(LDPC)　coded　physical-layer　network　coding　(PNC)　in　a　two-way　relay　channel　(TWRC).　In　particular,　we　decode　the　transmit　combination　of　two-user　messages　from　the　superimposed　signal　and　then　map　the　XOR　message　of　two　users.　By　exploiting　the　superposition　rules　of　PNC,　we　develop　hard　decision-based　and　reliability-based　decoding　algorithms,　i.e.,　modified　one-step　MLGD　(M-OSMLGD)　and　iterative　soft　reliability-based　decoding　(M-ISRB),　to　iteratively　update　the　combination　of　two-user　messages.　Moreover,　we　propose　an　improved　M-ISRB　(IM-ISRB)　decoding　to　update　the　external　reliability　of　the　combination　of　two-user　messages　in　each　iteration.　Simulation　results　show　that　the　proposed　decoding　algorithms　can　achieve　effective　an　trade-off　between　complexity　and　decoding　performance　for　LDPC-coded　PNC　systems.　©　1997-2012　IEEE.