On the capacity of interference channels with partial codebook knowledge

Shannon theoretic multi-user capacity problems are traditionally formulated under the assumption that all decoding nodes possess all codebooks. However, for certain networks such as cognitive ones, this may be an unrealistic assumption. We work towards understanding the impact of lack of codebook knowledge at some decoding nodes in the network. We do so by considering a two-user interference channel in which one of the receivers has no information about the codebook of the interfering transmitter, while the other receiver has both codebooks. We derive a novel outer bound for the special class of injective semi-deterministic interference channels which incorporates this codebook knowledge explicitly. For the linear deterministic channel, which models the Gaussian channel at high SNR, we demonstrate the surprising fact that non i.i.d. Bernoulli(1/2) points achieve points on the outer bound not achievable by Bernoulli(1/2) inputs. We then show that this is achievable to within a constant gap by a modified Han-Kobayashi scheme. We characterize the capacity region of the Gaussian noise channel to within 1/2 bit, even though we could not determine the set of optimal input distributions. Numerical evaluations suggest that if the non-oblivious transmitter uses a discrete input a larger sum-rate is achievable compared to the case where both users employ Gaussian codebooks or use time division in strong interference regime at high SNR.