Separate network coding for private and common messages from one source to two sinks

Ngai-Yeung and Erez-Feder independently derived the capacity region of network coding with a single source and two sinks, in which a common message is sent from the source to both sinks but each private message is sent to only the corresponding sink. In this paper, it is shown that the above capacity region can be achieved by separate linear coding such that three routes of private and common messages are perfectly separated. This means that each private message can be sent to the corresponding sink only by routing while the common message can be sent to both sinks by a relatively simple multicast linear network code.