Explicit capacity-achieving coding scheme for the Gaussian wiretap channel

We extend the Bellare-Tessaro coding scheme for a discrete, degraded, symmetric wiretap channel to a Gaussian wiretap channel. Denoting by SNR the signal-to-noise ratio of the eavesdropper's channel, the proposed scheme converts a transmission code of rate R for the channel of the legitimate receiver into a code of rate R-0.5 log(1+SNR) for the Gaussian wiretap channel. The conversion has a polynomial complexity in the codeword length and the proposed scheme achieves strong security. In particular, when the underlying transmission code is capacity achieving, this scheme achieves the secrecy capacity of the Gaussian wiretap channel.