Strong secrecy for interference channels : Achievable rate region and degrees of freedom

The achievable rate region and degrees of freedom are studied for interference channels with confidential messages under strong secrecy constraints. The problem is studied based on the framework of Han and Verd$\\acute{\\textrm{u}}$'s channel resolvability theory. It is shown that if the random binning rate for securing a confidential message is slightly above the resolution of its corresponding wiretapped channel, strong secrecy can be guaranteed. At first, the information-spectrum method introduced by Han and Verd$\\acute{\\textrm{u}}$ is generalized to an arbitrary interference channel to obtain a direct channel resolvability result. After specifying the channel transition probability, the derived resolvability results are shown to be the achievable strong secrecy rates for the stationary and memoryless interference channel. As an application, the secure degrees of freedom (SDOF) for the $K$-user Gaussian interference channel with confidential messages are investigated under strong secrecy constraints. It is shown that the optimal SDOF of the considered network is $\\frac{K-1}{2K-1}$ for each user, which equals to its counterpart with weak secrecy constraints. The optimal SDOF scheme is achieved by combining the resolvability-based secrecy coding and artificial noise alignment on the real line. A suboptimal ergodic secure alignment is also proposed for the time-varying interference channels to achieve a sum SDOF of $\\frac{K-3}{2K-2}$ for each user. Following the footsteps of Hayashi and of Bloch and Laneman, our results provide further evidence that channel resolvability can be a powerful and general framework for strong secrecy analysis in multiuser networks.