Channel Leakage and Fundamental Limits of Privacy Leakage for Streaming Data

In this paper, we first introduce the notion of channel leakage as the minimum mutual information between the channel input and channel output. As its name indicates, channel leakage quantifies the (minimum) information leakage to the malicious receiver. In a broad sense, it can be viewed as a dual concept of channel capacity, which characterizes the (maximum) information transmission to the targeted receiver. We obtain explicit formulas of channel leakage for the white Gaussian case and colored Gaussian case. We also study the implications of channel leakage in characterizing the fundamental limitations of privacy leakage for streaming data.