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In group communications, multiple processes first establish a group and then each process sends a message to multiple processes while receiving messages from multiple processes in the group. In addition, messages are required to be causally/totally delivered to each process. Due to the limited computation and communication resource, processes cannot send and receive as messages as the processes would like. We newly propose a notification-based data transmission procedure with two-phase slow start (TPSS) to efficiently exchange multimedia messages in a group so as to satisfy QoS requirement. In TPSS, the transmission rate of a process is increased by transmitting redundant data so that no data is lost even if some packets are lost.