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

Bin Dai,Yuan Luo,A J Han Vinck

doi:10.1155/2013/423619

Abstract

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.

Highlights

We investigate the wiretap channel in the presence of action-dependent states and noiseless feedback
Equivocation was first introduced into channel coding by Wyner in his study of wiretap channel [1], see Figure 1
It is a kind of degraded broadcast channels

Summary

Introduction

Equivocation was first introduced into channel coding by Wyner in his study of wiretap channel [1], see Figure 1. Measuring wiretapper’s uncertainty about the transmitted message by equivocation, the capacity-equivocation regions of the model of Figure 6 are provided both for the case where the channel input is allowed to depend noncausally on the state sequence and the case where it is restricted to causal dependence. The secrecy capacity Cs(c) of the model of Figure 6 with causal channel state information is denoted by. We calculate the secrecy capacity of a special case of the model of Figure 6 with causal channel state information. It is easy to see that the secrecy capacity Csc is increasing while q is getting larger

Conclusion

Proof of the Direct Part of Theorem 6

Proof of the Converse Part of Theorem 6

Size Constraint of the Auxiliary Random Variable in Theorem 6

Proof of the Direct Part of Theorem 9

Proof of the Converse Part of Theorem 9