On constant gaps for the K-pair user two-way Gaussian interference channel with interaction

In a K-pair-user two-way Gaussian interference channel (IC), 2K messages and 2K transmitters/receivers form a Gaussian K-user IC in the forward direction (K messages) and another Gaussian K-user IC in the backward direction (K messages) which operate simultaneously in full-duplex mode. All nodes are permitted to interact, i.e. adapt current channel inputs to past received signals. We derive a new sum-rate outer bound for linear deterministic and Gaussian noise channels allowing for interaction, but show that for symmetric scenarios and certain interference regimes (moderately weak and strong), non-interactive schemes achieve to within a constant gap of this outer bound. That is, interaction for symmetric channels in certain interference regimes may only improve the sum-rate by a constant number of bits per channel use.