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We study a number of two-user interference networks with multiple-antennatransmitters/receivers, transmitter side information in the form of linearcombinations (over finite-field) of the information messages, and two-hoprelaying. We start with a Cognitive Interference Channel (CIC) where one of thetransmitters (non-cognitive) has knowledge of a rank-1 linear combination ofthe two information messages, while the other transmitter (cognitive) hasaccess to a rank-2 linear combination of the same messages. This is referred toas the Network-Coded CIC, since such linear combination may be the result ofsome random linear network coding scheme implemented in the backbone wirednetwork. For such channel we develop an achievable region based on a few novelconcepts: Precoded Compute and Forward (PCoF) with Channel Integer Alignment(CIA), combined with standard Dirty-Paper Coding. We also develop a capacityregion outer bound and find the sum symmetric GDoF of the Network-Coded CIC.Through the GDoF characterization, we show that knowing "mixed data" (linearcombinations of the information messages) provides an unbounded spectralefficiency gain over the classical CIC counterpart, if the ratio of SNR to INRis larger than certain threshold. Then, we consider a Gaussian relay networkhaving the two-user MIMO IC as the main building block. We use PCoF with CIA toconvert the MIMO IC into a deterministic finite-field IC. Then, we use a linearprecoding scheme over the finite-field to eliminate interference in thefinite-field domain. Using this unified approach, we characterize the symmetricsum rate of the two-user MIMO IC with coordination, cognition, and two-hops. Wealso provide finite-SNR results which show that the proposed coding schemes arecompetitive against state of the art interference avoidance based on orthogonalaccess, for Rayleigh fading channels.

Structured Lattice Codes for Some Two-User Gaussian Networks with Cognition, Coordination and Two Hops