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We consider a random access network in which K nodes wish to send independent packets to an access point (AP). In this letter, a novel method of feedback construction and an adaptive retransmission protocol of collided packets are proposed, which enable efficient successive interference cancellation at the AP. We show that the optimal throughput efficiency of one is achievable by only exploiting log K bits of feedback from the AP to K nodes, while the maximum throughput efficiency of slotted ALOHA is known to be e ^-1 ≈ 0.37 for large K. Note that the proposed technique achieves the optimal throughput efficiency for any finite K, while the conventional techniques asymptotically achieve the optimal throughput efficiency only when K tends to infinity.