In　this　paper,　we　propose　a　generalized　channel　decoding　scheme　for　nonbinary　physical-layer　network　coding　(CD-NC)　in　two-way　relay　channels　(TWRCs),　where　two　source　nodes　A　and　B　exchange　their　nonbinary　symbols　via　a　relay.　The　two　sources　use　the　same　nonbinary　low-density　parity-check　(LDPC)　channel　code　over　the　integer　ring　$\mathbb　{Z}-M$　and　$M$-pulse-amplitude　modulation,　respectively.　The　existing　channel　decoding　schemes　for　nonbinary　network　coding　suffer　severe　rate　loss　compared　with　the　cut-set　bound　of　TWRC,　especially　in　the　low-to-medium　signal-to-noise　ratio　regime.　The　proposed　CD-NC　can　decrease　the　rate　loss.　Our　contributions　are　as　follows:　1)　We　develop　a　generalized　nonbinary　sum　product　algorithm　(G-SPA)　for　CD-NC　according　to　the　principle　of　virtual　encoding　of　the　superimposed　symbols.　Simulation　results　show　that　our　CD-NC　can　achieve　significant　performance　gains　over　the　conventional　nonbinary　network　coding　for　both　additive　white　Gaussian　noise　and　fading　channels;　and　2)　We　exploit　two-dimensional　fast-Fourier-transform-based　belief　propagation　(2-D-FFT-BP)　and　extended　min-sum　(EMS)　decoding　algorithms　to　reduce　the　decoding　complexity　of　G-SPA.　Simulation　results　show　that　the　2-D-FFT-BP　has　the　same　performance　as　G-SPA,　while　EMS　can　greatly　reduce　the　decoding　complexity　of　G-SPA　at　the　cost　of　slight　performance　degradation.　©　1967-2012　IEEE.