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This paper proposes a media access control method for a multipoint cyclic data gathering system, in which each node transmits its data to the base-station periodically. In such condition, by broadcasting ACK/NACK signals from the base-station, the proposed method ensures assignment of a time slot for each node once the node succeeds to transfer its data. It is confirmed that the proposed scheme reduces packet collisions and outperforms conventional slotted-ALOHA scheme in throughput of data even with ACK/NACK errors. Furthermore the proposed scheme realizes adaptive slot assignment under cyclostationary channel environment.