Physical-layer security over correlated erasure channels

Recent accomplishments in physical-layer security research have shown that channel coding for secrecy can be effectively combined with security at other layers, such as cryptography at the application layer, in order to provide a significant security enhancement to communication systems. The goal of this previous work was to inhibit the passive eavesdropper in the wiretap channel model by encoding the ciphertext using nonsystematic low-density parity-check (LDPC) codes prior to transmission and by exploiting the advantage of feedback for legitimate parties. The net result was propagation of a single packet erasure to the detriment of the entire message. The security enhancement was characterized assuming statistically independent packet erasure channels (PECs) for the legitimate receiver and the eavesdropper. In this paper, we go beyond these results by addressing correlated erasure events across the two channels in a wiretap feedback framework. The intuitive notion that high correlation across channels reduces secrecy is shown through the complete characterization of the correlated channel scenario. Furthermore, it is shown that security improvements are still achievable in the face of positive correlation by means of judicious physical-layer design, even when the eavesdropper has a better channel than the legitimate receiver.