It is helpful to understand the capability and limitation of NAT, but as we shall see, NAT can only provide uni-directional connectivity to the IP Internet. Figure 2 illustrates a typical scenario where a network is constructed using the reusable-IP address space and is attached to the IP Internet via a NAT gateway, .
Assume only owns a single IP address. Consider the case where a reusable-IP host (the initiator) is connecting to an IP host (the responder). A reusable-IP address that belongs to host is denoted , and an IP address that belongs to host is denoted . Assume already knows the IP address of . simply initiates the connection by sending a packet to . Suppose this is a TCP connection, and the packet sent by has a source port number and a destination port number . We denote this packet by (the transport protocol is omitted for simplicity). The goal of NAT is to represent in the IP Internet by . As this packet is forwarded by , replaces by its own IP address , and by an available port number on , say, . The resulting packet is and is forwarded out of the reusable-IP network. When a corresponding response packet is received by , simply replaces the destination address by and the destination port number by . Since each 16-bit port number on can be reused for different transport protocols, roughly 65,000 TCP and 65,000 UDP connections can be simultaneously active from initiating reusable-IP hosts to every port of every responding IP host even though only has one IP address.
In contrast, if is the initiator and is the responder, the situation becomes very different. Because the only IP address owned by the reusable-IP network is , a DNS application level gateway  for in-bound NAT must resolve the name lookup for to . Unfortunately, since can only refer to one reusable-IP host at any given time, with one IP address, NAT can only provide general in-bound connectivity to one responder in the entire reusable-IP network at a time. Since having one IP address is typical, NAT cannot provide acceptable in-bound connectivity.