This　paper　investigates　an　efficient　power　allocation　for　channel　decoding　algorithms　in　two-user　downlink　non-orthogonal　multiple　access　(NOMA).　We　consider　three　successive　interference　cancellation　(SIC)　algorithms　with　low-density　parity-check　(LDPC)　codes,　i.e.,　the　SIC　treats　interference　as　noise　(N-SIC)　algorithm,　the　SIC　treats　modulation　of　interference　signal　as　auxiliary　information　(J-SIC),　and　the　SIC　exchanges　the　external　decoding　information　of　the　signals　for　two　users　(E-SIC).　To　improve　the　decoding　accuracy,　we　propose　power　allocation　algorithms　for　SIC　decoding　based　on　fairness　index　and　outage　probability　respectively.　The　rate-fairness　of　users　is　also　optimized.　Simulation　results　show　that　the　iterative　E-SIC　can　achieve　a　significant　performance　gain　over　N-SIC　and　J-SIC,　and　this　gain　is　much　smaller　when　the　power　allocation　(PA)　is　used　in　the　three　SIC　decodings.　Moreover,　we　analyze　performance　bound　of　Polyanskiy-Poor-Verdu　(PPV)　finite-length　for　the　SIC　decodings.　It　provides　a　theoretical　analysis　for　the　optimization　of　frame　error　rate　(FER)　by　power　allocation.