Physical-Layer Security over Correlated Erasure Channels

We explore the additional security obtained by noise at the physical layer in a wiretap channel model setting. Security enhancements at the physical layer have been proposed recently using a secrecy metric based on the degrees of freedom that an attacker has with respect to the sent ciphertext. Prior work focused on cases in which the wiretap channel could be modeled as statistically independent packet erasure channels for the legitimate receiver and an eavesdropper. In this paper, we go beyond the state-of-the-art by addressing correlated erasure events across the two communication channels. The resulting security enhancement is presented as a function of the correlation coefficient and the erasure probabilities for both channels. It is shown that security improvements are achievable by means of judicious physical-layer design even when the eavesdropper has a better channel than the legitimate receiver. The only case in which this assertion may not hold is when erasures are highly correlated across channels. However, we are able to prove that correlation cannot nullify the expected security enhancement if the channel quality of the legitimate receiver is strictly better than that of the eavesdropper.

💡 Research Summary

The paper investigates how physical‑layer noise can be exploited to increase secrecy in a wiretap setting when packet erasures on the legitimate (Bob) and eavesdropper (Eve) links are statistically correlated. Building on prior work that used the “degrees of freedom” (DoF) metric—i.e., the number of bits an eavesdropper must guess to recover the ciphertext—the authors extend the analysis from independent erasure channels to a correlated packet‑erasure channel (PEC) model.

The system model consists of an Alice that compresses and encrypts a message, splits it into k‑bit blocks, scrambles each block with a random invertible matrix, and encodes the result with a systematic (N,k) low‑density parity‑check (LDPC) code. A carefully chosen puncturing pattern R of size |R|=N−k removes exactly N−k coded bits, leaving n=k bits to be transmitted. These bits are interleaved across η packets of length α, forming the transmitted vector X. Bob receives X over a memoryless PEC with erasure probability δ, and can request retransmissions through an authenticated feedback channel (ARQ) until all packets are error‑free. Eve observes the same transmission over a second PEC with erasure probability ε; she also sees any retransmissions but cannot request them.

The key novelty is the introduction of a correlation coefficient ρ between the binary erasure indicators E_m (Bob) and E_w (Eve). Using Pearson’s definition, ρ = (p_11 – δε) / √