  In this paper, the k-th order autoregressive moving average (ARMA(k))
Gaussian wiretap channel with noiseless causal feedback is considered, in which
an eavesdropper receives noisy observations of the signals in both forward and
feedback channels. It is shown that a variant of the generalized
Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback
Gaussian channel, achieves the same maximum rate for the same channel with the
presence of an eavesdropper. Therefore, the secrecy capacity is equal to the
feedback capacity without the presence of an eavesdropper for the feedback
channel. Furthermore, the results are extended to the additive white Gaussian
noise (AWGN) channel with quantized feedback. It is shown that the proposed
coding scheme achieves a positive secrecy rate. As the amplitude of the
quantization noise decreases to zero, the secrecy rate converges to the
capacity of the AWGN channel.
