We know that in the Han-Kobayashi region, the to be transmitted data is divided into two parts, private and common. So, what type of information does these parts contain ?
As far as I know, there is no difference between the data content in the private and common messages. One simply takes the bit streams to be transmitted (representing any type of data), split them into a private part and a common part, and then encode them as Han-Kobayashi proposed.
The difference lies in that the common message is encoded so it can be decoded at other receivers than the intended one. The purpose of the decoding is not to access its data content (at the application layer) but to remove interference (at the physical layer), and thereby enabling decoding of the messages that are truly of interest.