How to Break the Limits of Secrecy Constraints in Communication Networks?

In many communication networks, secrecy constraints usually incur an extra limit in capacity (or generalized degrees-of-freedom, GDoF), in the sense that a penalty in capacity (or GDoF) is incurred due to the secrecy constraints. Over the past decades a significant amount of effort has been made by the researchers to understand the limits of secrecy constraints in communication networks. In this work, we focus on how to break the limits of secrecy constraints in communication networks, i.e., how to remove the penalty in GDoF due to the secrecy constraints. We begin with three basic settings: a two-user symmetric Gaussian interference channel with confidential messages, a symmetric Gaussian wiretap channel with a helper, and a two-user symmetric Gaussian multiple access wiretap channel. Interestingly, in this work we show that adding common randomness at the transmitters can totally remove the penalty in sum GDoF or GDoF region of the three settings considered here. The results reveal that adding common randomness at the transmitters is a powerful way to break the limits of secrecy constraints in communication networks. Common randomness can be generated offline. The role of the common randomness is to jam the information signal at the eavesdroppers, without causing too much interference at the legitimate receivers. To accomplish this role, a new method of Markov chain-based interference neutralization is proposed in the achievability schemes utilizing common randomness. From the practical point of view, we hope to use less common randomness to break the limits of secrecy constraints. With this motivation, for most of the cases we characterize the minimal GDoF of common randomness to break the limits of secrecy constraints, based on our derived converses.