On the dispersions of the discrete memoryless interference channel

In this work, achievable dispersions for the discrete memoryless interference channel (DM-IC) are derived. In other words, we characterize the backoff from the Han-Kobayashi (HK) achievable region, the largest inner bound known to date for the DM-IC. In addition, we also characterize the backoff from Sato's region in the strictly very strong interference regime, and the backoff from Costa and El Gamal's region in the strong interference regime. To do so, Feinstein's lemma is first generalized to be applicable to the interference channel. Making use of the generalized Feinstein's lemma, it is found that the dispersions for the DM-IC can be represented by the information variances of eight information densities when HK message splitting is involved, and of six information densities for another encoding strategy. We also derive an outer bound that leverages on a known dispersion result for channels with random state by Ingber-Feder. It is shown that for the strictly very strong interference regime, the inner and outer bound have similar algebraic forms.