Chadi Assi — Page 5 | Search arXiv

arXiv2017

On the Achievable Secrecy Diversity of Cooperative Networks with Untrusted Relays

Cooperative relaying is often deployed to enhance the communication reliability (i.e., diversity order) and consequently the end-to-end achievable rate. However, this raises several security concerns when the relays are untrusted since they may have access to the relayed message. In this paper, we study the achievable secrecy diversity order of cooperative networks with untrusted relays. In particular, we consider a network with an N-antenna transmitter (Alice), K single-antenna relays, and a single-antenna destination (Bob). We consider the general scenario where there is no relation between N and K, and therefore K can be larger than N. Alice and Bob are assumed to be far away from each other, and all communication is done through the relays, i.e., there is no direct link. Providing secure communication while enhancing the diversity order has been shown to be very challenging. In fact, it has been shown in the literature that the maximum achievable secrecy diversity order for the adopted system model is one (while using artificial noise jamming). In this paper, we adopt a nonlinear interference alignment scheme that we have proposed recently to transmit the signals from Alice to Bob. We analyze the proposed scheme in terms of the achievable secrecy rate and secrecy diversity order. Assuming Gaussian inputs, we derive an explicit expression for the achievable secrecy rate and show analytically that a secrecy diversity order of up to min(N,K)-1 can be achieved using the proposed technique. We provide several numerical examples to validate the obtained analytical results and demonstrate the superiority of the proposed technique to its counterparts that exist in the literature.

cs.CR↗

arXiv2016

Nonlinear Interference Alignment in a One-dimensional Space

Real interference alignment is efficient in breaking-up a one-dimensional space over time-invariant channels into fractional dimensions. As such, multiple symbols can be simultaneously transmitted with fractional degrees-of-freedom (DoF). Of particular interest is when the one dimensional space is partitioned into two fractional dimensions. In such scenario, the interfering signals are confined to one sub-space and the intended signal is confined to the other sub-space. Existing real interference alignment schemes achieve near-capacity performance at high SNR for time-invariant channels. However, such techniques yield poor achievable rate at finite SNR, which is of interest from a practical point of view. In this paper, we propose a radically novel nonlinear interference alignment technique, which we refer to as Interference Dissolution (ID). ID allows to break-up a one-dimensional space into two fractional dimensions while achieving near-capacity performance for the entire SNR range. This is achieved by aligning signals by signals, as opposed to aligning signals by the channel. We introduce ID by considering a time-invariant MISO channel. This channel has a one-dimensional space and offers one DoF. We show that, by breaking-up the one dimensional space into two sub-spaces, ID achieves a rate of two symbols per channel use while providing $\frac{1}{2}$ DoF for each symbol. We analyze the performance of the proposed ID scheme in terms of the achievable rate and the symbol error rate. In characterizing the achievable rate of ID for the entire SNR range, we prove that, assuming Gaussian signals, the sum achievable rate is at most one bit away from the capacity. We present numerical examples to validate the theoretical analysis. We also compare the performance of ID in terms of the achievable rate performance to that of existing schemes and demonstrate ID's superiority.

cs.IT↗