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We consider the problem of communication over a three-user discrete memoryless interference channel (3-IC). The current known coding techniques for communicating over an arbitrary 3-IC are based on message splitting, superposition coding, and binning using independent and identically distributed (i.i.d.) random codebooks. In this paper, we propose a new ensemble of codes-partitioned coset codes (PCCs)-that possess an appropriate mix of empirical and algebraic closure properties. We develop coding techniques that exploit the algebraic closure property of PCC to enable interference alignment over general 3-IC. We analyze the performance of the proposed coding technique to derive an achievable rate region for the general discrete 3-IC. Additive and non-additive examples are identified for which the derived achievable rate region is the capacity, moreover, strictly larger than the current known largest achievable rate regions based on the i.i.d. random codebooks.

An Achievable Rate Region for the Three-User Interference Channel Based on Coset Codes