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**1 - 2**of**2**### On the Two-User Interference Channel With Lack of Knowledge of the Interference Codebook at One Receiver

"... Abstract — 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 distrib-uted ad hoc, cognitive, or heterogeneous networks. This paper considers the two-user interference channel with one ..."

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Abstract — 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 distrib-uted 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 identi-cally 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.

### i.i.d. Mixed Inputs and Treating Interference as Noise are gDoF Optimal for the Symmetric Gaussian Two-user Interference Channel

"... Abstract—While a multi-letter limiting expression of the ca-pacity region of the two-user Gaussian interference channel is known, capacity is generally considered to be open as this is not computable. Other computable capacity outer bounds are known to be achievable to within 1/2 bit using Gaussian ..."

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Abstract—While a multi-letter limiting expression of the ca-pacity region of the two-user Gaussian interference channel is known, capacity is generally considered to be open as this is not computable. Other computable capacity outer bounds are known to be achievable to within 1/2 bit using Gaussian inputs and joint decoding in the simplified Han and Kobayashi (single-letter) achievable rate region. This work shows that the simple scheme known as “treating interference as noise ” without time-sharing attains the capacity region outer bound of the symmetric Gaussian interference channel to within either a constant gap, or a gap of order O(log log(SNR)), for all parameter regimes. The scheme is therefore optimal in the generalized Degrees of Freedom (gDoF) region sense almost surely. The achievability is obtained by using i.i.d. mixed inputs (i.e., a superposition of discrete and Gaussian random variables) in the multi-letter capacity expression, where the optimal number of points in the discrete part of the inputs, as well as the optimal power split among the discrete and continuous parts of the inputs, are characterized in closed form. An important practical implication of this result is that the discrete part of the inputs behaves as a “common message ” whose contribution can be removed from the channel output, even though joint decoding is not employed. Moreover, time-sharing may be mimicked by varying the number of points in the discrete part of the inputs. I.