The semantic secrecy rate of the lattice Gaussian coding for the Gaussian wiretap channel

In this paper, we investigate the achievable semantic secrecy rate of existing lattice coding schemes, proposed in [6], for both the mod-Λ Gaussian wiretap and the Gaussian wiretap channels. For both channels, we propose new upper bounds on the amount of leaked information which provide milder sufficient conditions to achieve semantic secrecy. These upper bounds show that the lattice coding schemes in [6] can achieve the secrecy capacity to within ½ln e/2 nat for the mod-Λ Gaussian and to within ½(1 - ln (1 + SNRe / SNRe+1)) nat for the Gaussian wiretap channels where SNRe is the signal-to-noise ratio of Eve.