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The authors consider bounds for the capacity region of the Gaussian X Channel (XC), a system consisting of two transmit-receive pairs, where each transmitter communicates with both the receivers. They first classify the XC into two classes, the strong XC and the mixed XC. In the strong XC, either the direct channels are stronger than the cross channels or vice-versa, whereas in the mixed XC, one of the direct channels is stronger than the corresponding cross channel and vice-versa. After this classification, they give outer bounds on the capacity region for each of the two classes. This is based on the idea that when one of the messages is eliminated from the XC, the rate region of the remaining three messages are enlarged.
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