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This paper considers the multiple access of mobile users to a common wireless channel. The channel is slotted and the binary feedback (empty slot/nonempty slot) is sent to all accessing users. If a slot was not empty and only one user transmitted in it, the transmission is considered successful. Only the user, which had the successful transmission, receives information about its success. In the Introduction, the paper gives a review of known multiple-access algorithms for such a channel. Then our algorithm is constructed that has none of the weaknesses of the algorithms discussed in the Introduction. The algorithm is stable, in contrast to the ALOHA algorithm. It can work in a channel with capture and multiple reception. Without them, the algorithm has a throughput of 0.2891. It is shown how capture and multiple reception can increase the algorithm throughput to 0.6548 and decrease the packet delay for some fading models. The average packet delay and variance are found for two fading models. The models are Rayleigh fading with incoherent and coherent combining of joint interference power. The accessing traffic is Poisson.