In　this　paper,　we　propose　a　two-user　polar-coded　physical-layer　network　coding　(TU-PC-PNC)　scheme　for　the　Gaussian　multiple　access　channel　(GMAC)　to　enhance　the　transmission　reliability.　We　first　investigate　the　characteristics　of　polar　encoding　and　derive　the　concatenated　codeword　structure,　by　which　we　can　implement　the　message　exclusive　OR　(XOR)-based　PNC　via　code　construction　and　improve　the　channel　polarization　effect.　The　PNC-aided　decoding　rule　based　on　the　concatenated　codeword　is　then　invented　to　compute　the　initial　messages　for　recovery.　In　addition,　we　introduce　the　joint　optimization　framework　by　Monte　Carlo-based　method,　which　can　be　used　to　optimize　the　polar　code　and　power　allocation　with　maximized　sum　user　rate.　The　capacity　analysis　of　the　bit-channels　and　simulation　results　show　that　the　proposed　TU-PC-PNC　can　significantly　outperform　the　benchmark　scheme　by　more　than　1　dB　under　the　GMAC.　©　1967-2012　IEEE.