Secure Communications with Limited Common Randomness at Transmitters

In this work we consider common randomness-aided secure communications, where a limited common randomness is available at the transmitters. Specifically, we focus on a two-user interference channel with secrecy constraints and a wiretap channel with a helper, in the presence of a limited common randomness shared between the transmitters. For both settings, we characterize the optimal secure sum degrees-of-freedom (DoF) or secure DoF as a function of the DoF of common randomness. The results reveal that the secure sum DoF or secure DoF increases as the DoF of common randomness increases, bridging the gap between the extreme DoF point without common randomness and the other extreme DoF point with unlimited common randomness. The proposed scheme is a two-layer coding scheme, in which two sub-schemes are designed in two layers respectively, i.e., at two different power levels, utilizing common randomness in the first layer only. The role of common randomness is to jam partial information signal at the eavesdroppers, without causing interference at the legitimate receivers. To prove the optimality of the proposed scheme, a new converse is also derived in this work.

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