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A system with many nodes accessing a common receiver is considered. The forward channel is a time-slotted collision-type common radio channel. Due to a nonreliable forward channel, the receiver may misinterpret the actual event of a slot. For instance, an idle or a success slot can be interpreted as a conflict and a conflict or a success slot can be interpreted as an idle slot. The former kind of error is called a noise error, while the latter is called an erasure. Splitting multiple-access algorithms are introduced that can handle erasures as well as noise errors. A remarkable feature of the algorithms is that they ensure that, under stable operation, all packets are eventually successfully transmitted, including the erased packets (those packets that were involved in an erasure). The property that is exploited in devising these algorithms is that nodes whose packets were erased can detect that situation as they transmit and acknowledge that the slot was idle. Consequently, they can either retransmit immediately or wait until some agreed point in time (such as the end of a collision resolution interval) and then transmit. The performances of the proposed algorithms are evaluated according to the maximal throughput they can support for Poisson arrival process. The performance degradation due to erasures and noise errors is quantified.