On the capacity region of the two-user Interference Channel

One of the key open problems in network information theory is to obtain the capacity region for the two-user Interference Channel (IC). In this paper, new results are presented for this channel. First, a novel outer bound on the capacity region is given. It is shown that this outer bound is optimal in the strong interference regime. Moreover, by using the derived outer bound, some new capacity theorems are proved. Specifically, a mixed interference regime is identified for the general IC where decoding interference at one receiver and treating interference as noise at the other one is sum-rate optimal. Also, a class of one-sided ICs with weak interference is identified for which treating interference as noise is sum-rate optimal. Our new capacity theorems include the previously obtained results for the mixed Gaussian IC and the weak Gaussian one-sided IC as special cases. Next, some results are given on the Han-Kobayashi (HK) achievable rate region. The evaluation of this rate region is in general difficult. In this paper, a simple characterization of the HK rate region is derived for a novel very weak interference regime. It is shown that for this very weak interference regime, the achievable sum-rate due to the HK region is identical to the one given by the simple treating interference as noise strategy. Finally, by using a novel genie-aided technique, a noisy interference regime is identified for the general IC (non-Gaussian) where the sum-rate capacity is achieved by treating interference as noise at the receivers. This result includes the noisy interference regime previously obtained for the Gaussian channel as a special case.