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The interference channel with degraded message sets (IC-DMS) refers to a communication model, in which two senders attempt to communicate with their respective receivers simultaneously through a common medium, and one sender has complete and a priori (noncausal) knowledge about the message being transmitted by the other. A coding scheme that collectively has advantages of cooperative coding, collaborative coding, and dirty paper coding, is developed for such a channel. With resorting to this coding scheme, achievable rate regions of the IC-DMS in both discrete memoryless and Gaussian cases are derived. The derived achievable rate regions generally include several previously known rate regions as special cases. A numerical example for the Gaussian case further demonstrates that the derived achievable rate region offers considerable improvements over these existing results in the high-interference-gain regime.