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Popular multiple-access schemes for asynchronous users that access the channel at randomly or pseudorandomly chosen time instances are ALOHA and TH-PPM. To cope with the randomness of these signals can be challenging for a receiver. In this paper, an uncoordinated but deterministic multiple-access scheme is proposed that can eliminate some of these drawbacks. The principle of this scheme is that each user transmits with an individual pulse or packet rate, while the duty cycle of the user signals is kept very low. As the access to the channel is asynchronous, collisions will occur. An analytical expression is derived for the collision probability, which depends on the asynchronism between the users. Design rules are derived that make the collision probability independent of the asynchronism. In practical implementations, deviations from the design values for the user rates will occur, and the length of a data packet is limited; the impact of these aspects on the collision probability is discussed. Simulation of a sensor network scenario without transmit power control shows that the design rules that make the collision probability insensitive to the asynchronism also do this for the bit-error rate (BER). The comparison of simulation results for RDMA with binary antipodal modulation and random TH-PSK, which is related to TH-PPM, yields very similar bit-error rates.