Information Flow Decomposition in Feedback Systems: Linear Time-Invariant Systems with Gaussian Channels

In our companion paper [1], an information identity decomposition has been derived, which can be interpreted as a law of conservation of information flows in feedback systems. In this paper, we further investigate this decomposition result when specified to linear time-invariant(LTI) systems connected with additive white Gaussian noise(AWGN) channels. It is shown that the quantities in the decomposition are characterized in sensitivity function and the law of conservation is verified.