Non-orthogonal multiple access (NOMA) is a candidate multiple access scheme in 5G systems for the simultaneous access of tremendous number of wireless nodes. On the other hand, RF-enabled wireless energy harvesting is a promising technology for self-sustainable wireless nodes. In this paper, we consider a NOMA system where the near user harvests energy from the strong radio signal to power-on the information decoder. A generalized energy harvesting scheme is proposed by combining the conventional time switching and power splitting scheme. The achievable rate region of the proposed scheme is characterized under both constant and dynamic decoding power consumption models. If the decoding power is constant, the achievable rate region can be found by solving two convex optimization subproblems, and the regions for two special cases: time switching and power splitting, are characterized in closed-form. If the decoding power is proportional to data rate, the achievable rate region can be found by exhaustive search algorithm. Numerical results show that the achievable rate region of the proposed generalized scheme is larger than those of time switching scheme and power splitting scheme, and rate-dependent decoder design helps to enlarge the achievable rate region.