Journal of Applied Mathematics
Volume 2013 (2013), Article ID 423619, 17 pages
Research Article

Wiretap Channel in the Presence of Action-Dependent States and Noiseless Feedback

1School of Information Science and Technology, Southwest JiaoTong University, Chengdu 610031, China
2Institute for Experimental Mathematics, Duisburg-Essen University, Ellernstraße 29, 45326 Essen, Germany
3Computer Science and Engineering Department, Shanghai Jiao Tong University, Shanghai 200240, China

Received 29 November 2012; Accepted 3 January 2013

Academic Editor: Jin Liang

Copyright © 2013 Bin Dai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the wiretap channel in the presence of action-dependent states and noiseless feedback. Given the message to be communicated, the transmitter chooses an action sequence that affects the formation of the channel states and then generates the channel input sequence based on the state sequence, the message, and the noiseless feedback, where the noiseless feedback is from the output of the main channel to the channel encoder. The main channel and the wiretap channel are two discrete memoryless channels (DMCs), and they are connected with the legitimate receiver and the wiretapper, respectively. The transition probability distribution of the main channel depends on the channel state. Measuring wiretapper’s uncertainty about the message by equivocation, the capacity equivocation regions are provided both for the case where the channel inputs are allowed to depend noncausally on the state sequence and the case where they are restricted to causal dependence. Furthermore, the secrecy capacities for both cases are formulated, which provide the best transmission rate with perfect secrecy. The result is further explained via a binary example.