The design of random media access control (MAC) protocol has been attractinggreat attention for satellite communication networks, where the propagation delay is long and the traffic load is varying. Advanced coded random access schemes tend to provide re?source allocation strategies for massive uncoordinated devices, where multiple packet repli?cas from each user are transmitted in random slots of the frame and successive interference cancellation (SIC) iterations are tracked to recover collided packets at the receiver. It is as?sumed that each active user just has a single information packet to be transmitted. In this pa?per, an MAC layer random access scheme named Multi-Packets Transmitted Irregular Repe?tition Slotted Aloha (M-IRSA) is proposed. Different from the existing advanced random ac?cess schemes, the M-IRSA scheme supports various number of packet transmission per user by using pre-coding procedure. Joint decoding combined with SIC iterations and local de?coding is analyzed. The simulation results show that the proposed scheme is more efficient compared with the IRSA scheme without packet loss rate (PLR) loss.