Ergodic Secret Alignment

In this paper, we introduce two new achievable schemes for the fading multiple access wiretap channel (MAC-WT).In the model that we consider, we assume that perfect knowledge of the state of all channels is available at all the nodes in a causal fashion.Our schemes use this knowledge together with the time-varying nature of the channel model to align the interference from different users at the eavesdropper perfectly in a one-dimensional space while creating a higher dimensionality space for the interfering signals at the legitimate receiver, hence allowing for better chance of recovery.While we achieve this alignment through signal scaling at the transmitters in our first scheme (scaling-based alignment), we let nature provide this alignment through the ergodicity of the channel coefficients in the second scheme [ergodic secret alignment (ESA)] [1], [2].For each scheme, we obtain the resulting achievable secrecy rate region.We show that the secrecy rates achieved by both schemes in the two-user fading MAC-WT scale with signal-to-noise ratio (SNR) as 1 2 log(SNR).Hence, we show the suboptimality of the independent identically distributed (i.i.d.) Gaussian signaling-based schemes with and without cooperative jamming by showing that the secrecy rates achieved using i.i.d.Gaussian signaling with cooperative jamming do not scale with SNR.In addition, we introduce an improved version of our ESA scheme where we incorporate cooperative jamming to achieve higher secrecy rates.Moreover, we derive the necessary optimality conditions for the power control policy that maximizes the secrecy sum rate achievable by our ESA scheme when used solely and with cooperative jamming.Finally, we discuss the extension of the proposed schemes to the case where there are more than two users and show that, for the -user fading MAC-WT, each of the two schemes achieves secrecy sum rate that scales with SNR as 1 log(SNR).