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This paper presents a new coding scheme and a corresponding achievable rate region for a class of deterministic interference channels with three sender-receiver pairs (3-DIC). The codebook structure uses rate splitting, Marton coding, and superposition coding. The receivers use interference decoding to exploit the structure of the combined interference signal without uniquely decoding any of the interfering messages partly or fully. The corresponding rate region is shown to contain all previously known achievable rate regions for the deterministic interference channel. The scheme can be extended to general discrete memoryless interference channels and provides a natural generalization of the Han-Kobayashi scheme for the two-user- pair case.