Secrecy Capacity of Wiretap Channels with Additive Colored Gaussian Noise

Abstract

Wyner has shown in his seminal paper on (discrete memoryless) wiretap channels that if the channel between the sender and an eavesdropper is a degraded version of the channel between the sender and the legitimate receiver, then the sender can reliably and securely transmit a message to the receiver, while the eavesdropper obtains absolutely no information about the message. Later, Leung-Yan-Cheong and Hellman extended Wyner's result to the case where the noise is white Gaussian. In this paper we extend the white Gaussian wiretap channel to the colored Gaussian case and show the finite block length secrecy capacity of colored Gaussian wiretap channels. We also show an asymptotic lower bound on the secrecy capacity of a specific colored Gaussian wiretap channel for which optimum power allocation can be found by water filling.