In order to achieve the Han-Kobayashi rate region for the two-user interference channel each transmitter splits its message into two sub-messages, each drawn from an independent codebook. Generalizing this idea to the K-user interference channel implies that 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K-1</sup> codebooks should be allocated to each transmitter, where each of them carries the message that is public to one of the subsets of the K-1 non-designated receivers. While such a rate-splitting scheme yields the best known achievable rate region (with random coding), optimizing a rate-related utility function over this region presents certain challenges stemming from the computational complexities and the distributed nature of interference channels. This paper introduces the notion of partial group decoding which offers a practical rate optimization strategy over this achievable rate region and mitigates these challenges. The merits of partial group decoders are demonstrated through treating the problem of optimal rate allocation with fairness constraints.
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