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 derived for this channel. As a first result, a noisy interference regime is given for the general IC where the sum-rate capacity is achieved by treating interference as noise at the receivers. To obtain this result, a single-letter outer bound in terms of some auxiliary random variables is first established for the sum-rate capacity of the general IC and then those conditions under which this outer bound is reduced to the achievable sum-rate given by the simple treating interference as noise strategy are specified. The main benefit of this approach is that it is applicable for any two-user IC (potentially non-Gaussian). For the special case of Gaussian channel, our result is reduced to the noisy interference regime that was previously obtained. 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 some special cases, specifically, for a novel very weak interference regime. As a remarkable characteristic, 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.