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Secrecy capacity of the first-order autoregressive moving average Gaussian channel with feedback

In this paper, we consider the first-order autoregressive moving average Gaussian channel with perfect causal feedback where an eavesdropper receives noisy observations of the channel inputs and outputs. We show that the secrecy capacity is equal to the feedback capacity without the presence of eavesdropper. Furthermore, we explicitly construct the secrecy capacity-achieving feedback code, which is deterministic and simple to implement.