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We study a two-user cognitive interference channel (CIC) where one of thetransmitters (primary) has knowledge of a linear combination (over anappropriate finite field) of the two information messages. We refer to thischannel model as Network-Coded CIC, since the linear combination may be theresult of some linear network coding scheme implemented in the backbone wirednetwork.In this paper, we characterize the generalized degrees of freedom(GDoF) for the Gaussian Network-Coded CIC. For achievability, we use the novelPrecoded Compute-and-Forward (PCoF) and Dirty Paper Coding (DPC), based onnested lattice codes. As a consequence of the GDoF characterization, we showthat knowing "mixed data" (linear combinations of the information messages)provides a {\em multiplicative} gain for the Gaussian CIC, if the power ratioof signal-to-noise (SNR) to interference-to-noise (INR) is larger than certainthreshold. For example, when $\SNR=\INR$, the Network-Coded cognition yields a100% gain over the classical Gaussian CIC.

Generalized Degrees of Freedom for Network-Coded Cognitive Interference Channel