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The sum capacity of the general K-user Gaussian Interference Channel (GIC) is known only when the channel coefficients are such that treating interference as noise (TIN) is optimal. The Han-Kobayashi (HK) scheme achieves the best known achievable rate region for the K-user interference channel (IC). Simple HK schemes are HK schemes with Gaussian signaling, no time sharing, and no private-common power splitting. The class of simple HK (S-HK) schemes includes the TIN scheme and schemes that involve various levels of interference decoding and cancellation at each receiver. We derive conditions under which simple HK schemes achieve sum capacity for general K-user Gaussian ICs. These results generalize existing sum capacity results for the TIN scheme to the class of simple HK schemes.

Channel Conditions for the Optimality of Interference Decoding Schemes for K-user Gaussian Interference Channels