In　this　paper,　we　propose　a　joint　polar　coding　and　physical　network　coding　(PNC)　for　two−user　downlink　non−orthogonal　multiple　access　(PN−DNOMA)　channels,　since　the　successive–interference–cancellation–aided　polar　decoding　cannot　be　optimal　for　finite　blocklength　transmissions.　In　the　proposed　scheme,　we　first　constructed　the　XORed　message　of　two　user　messages.　Then,　the　XORed　message　was　superimposed　with　the　message　of　the　weak　User　2　for　broadcast.　By　doing　so,　we　can　utilize　the　PNC　mapping　rule　and　polar　decoding　to　directly　recover　the　message　of　User　1,　while　at　User　2,　we　equivalently　constructed　a　long−length　polar　decoder　to　obtain　its　user　message.　The　channel　polarization　and　decoding　performance　can　be　greatly　improved　for　both　users.　Moreover,　we　optimized　the　power　allocation　of　the　two　users　with　their　channel　conditions　by　considering　the　user　fairness　and　the　performance.　The　simulation　results　showed　that　the　proposed　PN−DNOMA　can　achieve　performance　gains　of　about　0.4−0.7　dB　over　the　conventional　schemes　in　two−user　downlink　NOMA　systems.　©　2023　by　the　authors.