Interference Alignment for Secrecy

This paper studies the frequency/time selective <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -user Gaussian interference channel with secrecy constraints. Two distinct models, namely the interference channel with confidential messages and the interference channel with an external eavesdropper, are analyzed. The key difference between the two models is the lack of channel state information (CSI) of the external eavesdropper. Using interference alignment along with secrecy precoding, it is shown that each user can achieve non-zero secure degrees of freedom (DoF) for both cases. More precisely, the proposed coding scheme achieves [( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -2)/(2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -2)] secure DoF with probability one per user in the confidential messages model. For the external eavesdropper scenario, on the other hand, it is shown that each user can achieve [( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -2)/(2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> )] secure DoF in the ergodic setting. Remarkably, these results establish the positive impact of interference on the secrecy capacity region of wireless networks.