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In this paper, we study the throughput enhancement in a wireless slotted ALOHA system, where all users transmit space-time coded information sequences and the destination is able to separate a given number of collided packets. These users operate with the slotted ALOHA protocol to access to the wireless channel resulting in a high probability of collision. To increase the packet throughput of such a system, we propose to separate the collided packets at the destination with a successive interference canceller that performs joint detection: channel estimation and data detection. The multi-user detector that we propose exploits the benefits of both the collision processing and the space-time signature induced by the Alamouti-type space-time block coding to improve the throughput. The validity of the proposed algorithm is highlighted by simulation results.