Successive interference cancellation (SIC) is considered to be a promising technique to mitigate multi-user interference and achieve concurrent uplink transmissions, but the optimal power allocation (PA) issue for SIC users is not well addressed. In this article, we focus on the optimization of the PA ratio of users on an SIC channel and analytically obtain the optimal PA ratio with regard to the signal-to-interference-plus-noise ratio (SINR) threshold for successful demodulation and the sustainable demodulation error rate. Then, we design an efficient resource allocation (RA) scheme using the obtained optimal PA ratio. Finally, we compare the proposal with the near-optimum RA obtained by a simulated annealing search and the RA scheme with random PA. Simulation results show that our proposal achieves a performance close to the near-optimum and much higher performance than the random scheme in terms of total utility and Jain"s fairness index. To demonstrate the applicability of our proposal, we also simulate the proposal in various network paradigms, including wireless local area network, body area network, and vehicular ad hoc network.