On the Two-User Interference Channel With Lack of Knowledge of the Interference Codebook at One Receiver

In multiuser information theory, it is often assumed that every node in the network possesses all codebooks used in the network. This assumption may be impractical in distributed ad hoc, cognitive, or heterogeneous networks. This paper considers the two-user interference channel with one oblivious receiver (IC-OR), i.e., one receiver lacks knowledge of the interfering cookbook, whereas the other receiver knows both codebooks. This paper asks whether, and if so how much, the channel capacity of the IC-OR is reduced compared with that of the classical IC where both receivers know all codebooks. A novel outer bound is derived and shown to be achievable to within a gap for the class of injective semideterministic IC-ORs; the gap is shown to be zero for injective fully deterministic IC-ORs. An exact capacity result is shown for the general memoryless IC-OR when the nonoblivious receiver experiences very strong interference. For the linear deterministic IC-OR that models the Gaussian noise channel at high SNR, nonindependent identically distributed. Bernoulli(1/2) input bits are shown to achieve points not achievable by i.i.d. Bernoulli(1/2) input bits used in the same achievability scheme. For the real-valued Gaussian IC-OR, the gap is shown to be at most 1/2 bit per channel use, even though the set of optimal input distributions for the derived outer bound could not be determined. Toward understanding the Gaussian IC-OR, an achievability strategy is evaluated in which the input alphabets at the nonoblivious transmitter are a mixture of discrete and Gaussian random variables, where the cardinality of the discrete part is appropriately chosen as a function of the channel parameters. Surprisingly, as the oblivious receiver intuitively should not be able to jointly decode the intended and interfering messages (whose codebook is unavailable), it is shown that with this choice of input, the capacity region of the symmetric Gaussian IC-OR is to within 1/2 log (12πe)≈ 3.34 bits (per channel use per user) of an outer bound for the classical Gaussian IC with full codebook knowledge at both receivers.