LAUSR

Most of the existing information-theoretic secure key generation schemes have characterized maximum achievable secrecy rate or secrecy capacity over noiseless public broadcast channels. However, in many practical systems even legitimate nodes have to communicate over noisy channels. In this letter, we propose a secret key generation scheme based on secure network coding in Gaussian wiretap channels. We prove that even when the channel from the sender to the receiver is weaker than that to the eavesdropper, secret communication at a positive rate is still possible if the condition $\sigma _{1} < \sqrt {\sigma _{2}^{2}+\sigma _{3}^{2}}$ is satisfied. Moreover, we establish an upper bound on the secrecy leakage rate after privacy amplification using double-layered random coding and joint typicality encoding and decoding over noisy public channels. The proof of achievability and the converse is given to demonstrate that the proposed scheme can achieve information-theoretic security.