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A new theory for deadlock-free multicast routing especially used for on-chip interconnection network (NoC) is presented in this paper. The NoC router hardware solution that enables the deadlock-free multicast routing without utilizing virtual channels is introduced formally. The special characteristic of the NoC is that, wormhole packets can cut-through at flit-level and can be interleaved in the same channel with other flits of different packets by multiplexing it using a rotating flit-by-flit arbitration. The routing paths of each flit can be guaranteed correct because flits belonging to the same packet are labeled with the same local Id-tag on every communication channel. Hence, multicast deadlock problem can be solved at each router by further applying a hold-release tagging mechanism to control and manage conflicting multicast requests.