In　this　paper,　we　propose　a　polarization-aided　polar　coding　scheme　over　non-orthogonal　multiple　access　channels　operated　with　physical-layer　network　coding　(PN-NOMA),　where　M　users　adopt　polar　coding　for　transmission.　By　exploiting　the　characteristic　of　PNC　and　polar　encoding,　we　found　that　the　polar　code　at　the　users　can　be　seen　as　nested　codes　and　sub-codeword　of　a　larger　polar　code.　It　enables　us　to　construct　a　single　(virtual)　polar　code　at　the　receiver,　which　has　the　length　M　times　longer　than　that　of　the　original　user　codes.　In　this　way,　we　can　decode　all　the　user　messages　within　this　single　polar　code.　The　channel　polarization　effect　as　well　as　the　decoding　performance　can　be　improved.　We　further　propose　a　Monte　Carlo-based　code　construction　for　the　virtual　polar　code　with　user　channel　coefficients,　and　short　nested　user　codes　can　be　individually　derived　from　this　code.　Simulation　results　show　that　the　proposed　PN-NOMA　can　achieve　significant　performance　gains　of　more　than　0.5　dB　as　compared　to　conventional　polar-coded　NOMA　(PC-NOMA)　over　power-imbalanced　channels,　and　this　gain　is　more　than　2　dB　over　Rayleigh　fading　channels.　IEEE