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We consider random access in wireless networks under a physical interference model, wherein a receiver is capable of power-based capture, i.e., a packet can be correctly decoded in the presence of multiple transmissions if the received signal-to-interference-plus-noise ratio (SINR) exceeds a threshold. We propose a splitting algorithm that varies the transmission power of users on the basis of quaternary channel feedback (idle, success, capture, and collision). We show that our algorithm achieves a maximum stable throughput of 0.5518. Simulation results demonstrate that our algorithm achieves higher throughput and lower delay than those of first-come-first-serve and residual-energy-based splitting algorithms with uniform transmission power.