Wiretap feedback channels

The secrecy capacity of the wiretap channel with rate-limited feedback

Ehsan Ardestanizadeh, Massimo Franceschetti, Tara Javidi, and Young-Han Kim

IEEE Transactions on Information Theory, vol. 55, no. 12, pp. 5353–5361, December 2009.
Preliminary results appeared in Proceedings of IEEE International Symposium on Information Theory, pp. 101–105, Toronto, Canada, July 2008.
IEEE AbstractPlus.

This paper studies the problem of secure communication over a wiretap channel p(y,z|x) with a secure feedback link of rate R_f , where is the channel input, and and are channel outputs observed by the legitimate receiver and the eavesdropper, respectively. It is shown that the secrecy capacity, the maximum data rate of reliable communication while the intended message is not revealed to the eavesdropper, is upper bounded as

$C_s(R_f) leq max_{p(x)}min { I(X;Y), I(X;Y|Z) + R_f }.$

The proof of the bound crucially depends on a recursive argument which is used to obtain the single-letter characterization. This upper bound is shown to be tight for the class of physically degraded wiretap channels. A capacity-achieving coding scheme is presented for this case, in which the receiver securely feeds back fresh randomness with rate R_f , generated emph{independent} of the received channel output symbols. The transmitter then uses this shared randomness as a secret key on top of Wyner's coding scheme for wiretap channels without feedback. Hence, when a feedback link is available, the receiver should allocate all resources to convey a new key rather than sending back the channel output.