minPIC: Towards Optimal Power Allocation in Multi-User Interference Channels

6G envisions massive cell-free networks with spatially nested multiple access (MAC) and broadcast (BC) channels without centralized coordination. This makes optimal resource allocation across power, subcarriers, and decoding orders crucial for interference channels (ICs), where neither transmitters nor receivers can cooperate. Current orthogonal multiple access (OMA) methods, as well as non-orthogonal (NOMA) and rate-splitting (RSMA) schemes, rely on fixed heuristics for interference management, leading to suboptimal rates, power inefficiency, and scalability issues. This paper proposes a novel minPIC framework for optimal power, subcarrier, and decoding order allocation in general multi-user ICs. Unlike existing methods, minPIC eliminates heuristic SIC order assumptions. Despite the convexity of the IC capacity region, fixing an SIC order induces non-convexity in resource allocation, traditionally requiring heuristic approximations. We instead introduce a dual-variable-guided sorting criterion to identify globally optimal SIC orders, followed by convex optimization with auxiliary log-det constraints, efficiently solved via binary search. We also demonstrate that minPIC could potentially meet the stringent high-rate, low-power targets of immersive XR and other 6G applications. To the best of our knowledge, minPIC is the first algorithmic realisation of the Pareto boundary of the SIC-achievable rate region for Gaussian ICs, opening the door to scalable interference management in cell-free networks.