The Gaussian Interference Channel with lack of codebook knowledge at one receiver: Symmetric capacity to within a gap with a PAM input

The study of the two-user Gaussian Interference Channel (IC) where one receiver lacks knowledge of the interfering codebook, also dubbed the IC with an oblivious receiver (IC-OR), is motivated by: (1) in heterogeneous, cognitive, distributed or dynamic networks, assuming that every node posses codebooks of every other node may not be practical, and (2) it is not clear whether and how much lack of codebook knowledge would affect the Han and Kobayashi (HK) achievable scheme, which involves joint decoding of intended and interfering messages and which appears not possible if nodes do not possess all codebooks. To address these issues, we evaluate a simplified HK (where the oblivious receiver treats interference as noise) with mixed inputs at the non-oblivious transmitter, i.e., a mixture of discrete and Gaussian random variables, where the power split between the two and the number of points of the discrete part are carefully chosen as a function of the channel parameters. The oblivious transmitter uses a purely Gaussian input. Surprisingly, for this choice of inputs, the capacity region of the symmetric Gaussian IC-OR is shown to be within 1 over 2 log (12πe) ≈ 3.34 bits of the best known outer bound for the classical Gaussian IC with full codebook knowledge at both receivers. Interestingly, this shows that a simplified HK where one receiver is restricted to treat interference as noise loses at most 1 over 2 log (12πe) ≈ 3.34 bits in performance. Moreover, the discrete part of the input behaves like a “common message” even though it is not jointly decoded (together with the intended messages) at the oblivious receiver.