We consider a memoryless narrowband Gaussian interference channel (GIC) where K single antenna users corn municate with their respective receivers using Gaussian code books. Each receiver employs a successive group decoder with a specified complexity constraint, to decode its designated user. It is aware of the coding schemes employed by all other users and may choose to decode some or all of them only if it deems that doing so will aid the decoding of its desired user. For a GIC with predetermined rates for all users, we obtain the minimum outage probability decoding strategy at each receiver, which satisfies the imposed complexity constraint and reveals the optimal channel dependent subset of interferers that must be decoded along with the desired user. We then consider the rate allocation problem over the GIC and design two distributed rate allocation algorithms which yield the symmetric fair rate allocation and the max min fair rate allocation, respectively.
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