Compute-and-Forward Can Buy Secrecy Cheap
This addresses secure communication for multiple transmitters in wireless networks, offering a practical improvement over prior methods that were limited to high SNR.
The paper tackles secure communication in a Gaussian multiple access channel with an eavesdropper by proposing a new lattice alignment scheme based on compute-and-forward that works at any finite SNR, achieving a secure sum rate that scales with log(SNR) and outperforms random coding in most SNR regimes.
We consider a Gaussian multiple access channel with $K$ transmitters, a (intended) receiver and an external eavesdropper. The transmitters wish to reliably communicate with the receiver while concealing their messages from the eavesdropper. This scenario has been investigated in prior works using two different coding techniques; the random i.i.d. Gaussian coding and the signal alignment coding. Although, the latter offers promising results in a very high SNR regime, extending these results to the finite SNR regime is a challenging task. In this paper, we propose a new lattice alignment scheme based on the compute-and-forward framework which works at any finite SNR. We show that our achievable secure sum rate scales with $\log(\mathrm{SNR})$ and hence, in most SNR regimes, our scheme outperforms the random coding scheme in which the secure sum rate does not grow with power. Furthermore, we show that our result matches the prior work in the infinite SNR regime. Additionally, we analyze our result numerically.