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It is well known that without admission control, network congestion is bound to occur. However, to implement admission control is difficult in IP-based networks, which are constructed out of the end-to-end principle, and semantics of most major signaling protocols can only be interpreted at the edge of the network. Even if routers can perform admission control internally, the path computation and the state updating activities required for setting up and tearing down each flow will overwhelm the network. A new QoS architecture, called a nonblocking network, has been proposed recently, and it requires no internal admission control and can still offer hard QoS guarantees. In this architecture, as long as each edge node admits not more than a specified amount of traffic, the network will never experience link congestion. For multicast networks, the main problem with this approach is low throughput. Conventional tree-based multicast routing algorithms lead to a throughput so low that the nonblocking concept is rendered impractical. In this paper, we show how network coding can solve this problem. We demonstrate that a nonblocking unicast network and a multicast network share the same optimal paths, and that a nonblocking multicast network with network coding can admit the same amount of traffic as a nonblocking unicast network. The above conclusions apply to explicit-routing (MPLS-like) and shortest-path routing (IP-like) networks.