In 1975, Carleial presented a special case of an interference channel, called the very strong interference regime, in which the interference does not reduce the capacity of the constituent point-to-point Gaussian channels. In this paper, we show that in the strictly very strong interference regime, the dispersions are similarly unaffected. More precisely, in this paper, we characterize the second-order coding rates of the Gaussian interference channel in the strictly very strong interference regime. In other words, we characterize the speed of convergence of rates of optimal block codes toward a boundary point of the (rectangular) capacity region. These second-order coding rates are expressed in terms of the average probability of error and variances of appropriately defined information densities which coincide with the dispersion of the (single-user) Gaussian channel. This allows us to conclude that the dispersions are unaffected by interference in this channel model.

Recent results have shown that feedback can significantly increase the capacity of interference networks. This paper considers the impact of noise on such gains due to feedback. In particular, this paper considers the two-user linear deterministic interference channel with noisy feedback, as a stepping stone to characterize the approximate capacity region for the two-user Gaussian interference channel with noisy feedback. First, the capacity region for the symmetric linear deterministic interference channel with noisy feedback is obtained. It is shown that noisy feedback enlarges the capacity region if and only if the number of feedback bits l is greater than a certain threshold l*. It is found that, excluding the regime (1/2) ≤ α ≤ 2, where α is the normalized interference level, in which even full feedback does not increase symmetric capacity, this threshold l* is equal to the per-user symmetric capacity without feedback. One of the key ideas is a novel converse outer bounding technique for the weighted sum rates 2R1+ R2and R1+ 2R2. These results and the techniques developed for the linear deterministic model are then applied to characterize inner bounds and outer bounds for the symmetric Gaussian interference channel with noisy feedback. The outer bounds are shown to be at most 4.7 b/s/Hz away from the achievable rate region. As a corollary, the generalized-degrees-of-freedom region, which approximates the capacity region of the symmetric Gaussian interference channel at high SNR, is found.

The second-order asymptotics of the Gaussian interference channel in the strictly very strong interference regime are considered. The rates of convergence to a given point on the boundary of the (first-order) capacity region are determined. These rates are expressed in terms of the average probability of error and variances of selected modified information densities which coincide with the dispersion of the (single-user) Gaussian channel. Interestingly, under the strictly very strong interference assumption, the intuition that receivers can decode messages from non-intended transmitters carries over to the second-order analysis.

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.

The linear deterministic interference channel (LD-IC) with partial feedback is considered. Partial feedback for the LD-IC models a scenario in which the top l most-significant-bits of the channel output of receiver j are received as feedback at transmitter j, for j = 1, 2. The rationale for studying the LD-IC with partial feedback comes from the fact that it is a good approximation to the Gaussian interference channel with output feedback corrupted by additive white Gaussian noise (commonly referred to as noisy feedback). The main contribution of this paper is a characterization of the sum-capacity of the symmetric LD-IC with partial feedback. The differences between the models of partial feedback and rate-limited feedback are emphasized and highlighted by comparing the corresponding sum-capacities, which are shown to differ in general.