Can channel output feedback enhance the secrecy capacity of the finite state Markov wiretap channel with delayed state feedback?

Viswanathan has shown that the practical mobile communication system can be modeled as the finite state Markov channel (FSMC) with delayed feedback, where the receiver perfectly knows the channel state information (CSI) which undergoes a Markov process, and the receiver sends the CSI and his own channel output back to the transmitter after some time delay. Viswanathan found that the delayed feedback of the channel output does not help to increase the capacity of the FSMC with only delayed state feedback. Does this still holds when an additional eavesdropper is considered? In order to answer this question, in this paper, we study the finite state Markov wiretap channel (FSM-WC) with delayed feedback, where the CSI is perfectly known by the legitimate receiver and the eavesdropper, and the legitimate receiver sends the CSI and his own channel output back to the transmitter after some time delay. Inner and outer bounds on the secrecy capacity of this model are provided, and we show that these bounds meet if the eavesdropper's received channel output is a degraded version of the legitimate receiver's. Furthermore, we find that the legitimate receiver's delayed channel output feedback helps to enhance the secrecy capacity of the degraded FSM-WC with only delayed state feedback.