In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf . We shown that the secrecy capacity is bounded. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving scheme is based on both the Wyner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. Finally, we consider several special cases. When state information is available only at the legitimate receiver, the analysis suggests that unlike previous results involving feedback, it is better to use the feedback to send the state information to the transmitter (when possible), rather than send a random key.
In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf . We shown that the secrecy capacity is bounded. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving scheme is based on both the Wyner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. Finally, we consider several special cases. When state information is available only at the legitimate receiver, the analysis suggests that unlike previous results involving feedback, it is better to use the feedback to send the state information to the transmitter (when possible), rather than send a random key.
In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf. We shown that the secrecy capacity is bounded by Cs ≥ max {p(u|v) p(x|u,v)max min{I(U;Y|v) - I(U;Z|V) + H(V|Z) + Rf, I(U;Y|V)},p(u)p(x|u,v)max min{H(V|Z,U) + Rf, I(U;Y|V)}}. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving scheme is based on both the Wyner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. Finally, we consider several special cases. When state information is available only at the legitimate receiver, the analysis suggests that unlike previous results involving feedback, it is better to use the feedback to send the state information to the transmitter (when possible), rather than send a random key.
In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and the legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf. We derive upper and lower bounds on the secrecy capacity and show that, when the channel to the eavesdropper is degraded, the bounds are tight and the secrecy capacity is completely characterized. The capacity achieving scheme is based on Wyner, Csiszár, and Körner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. The upper bound is more involved and requires a nontrivial recursive lemma extending previous results in the literature to include both state and feedback. We conclude the paper by showing that a few interesting known results can be seen as special cases of the above, as well as discussing the case where the source of local randomness at the encoder is limited.
This paper studies the problem of secure communication over a wiretap channel p(y,z|x) with a secure feedback link of rate Rf, where X is the channel input, and Y and Z are channel outputs observed by the legitimate receiver and the eavesdropper, respectively. It is shown that the secrecy capacity, the maximum data rate of reliable communication while the intended message is not revealed to the eavesdropper, is upper bounded as Cs(Rf) les maxmin/p(x) {I(X;Y), I(X;Y |Z) + Rf}. The proof of the bound crucially depends on a recursive argument which is used to obtain the single-letter characterization. This upper bound is shown to be tight for the class of physically degraded wiretap channels. A capacity-achieving coding scheme is presented for this case, in which the receiver securely feeds back fresh randomness with rate Rf, generated independent of the received channel output symbols. The transmitter then uses this shared randomness as a secret key on top of Wyner's coding scheme for wiretap channels without feedback. Hence, when a feedback link is available, the receiver should allocate all resources to convey a new key rather than sending back the channel output.
This paper studies the problem of secure communication over a degraded wiretap channel p(y, z|x) = p(y|x)p(z|y) with secure feedback link of rate Rf, where X is the channel input, and Y and Z are channel outputs observed by the legitimate receiver and the wiretapper respectively. The secrecy capacity is characterized as Cs{Rf) = maxmin{I(X; Y), I(X; Y|Z) + Rf}. p(x)equation. A capacity-achieving coding scheme is presented, in which the receiver securely feeds back fresh randomness with rate Rf, independent of the received channel output. The transmitter then uses the shared randomness as a secret key on top of Wynerpsilas coding scheme for wiretap channel without feedback. Hence, when the receiver has a means of interacting with the transmitter, he should allocate all resources to convey a new key rather than sending back the channel output. For the converse, a recursive argument is used to obtain the single-letter characterization.
We introduce the wiretap channel with action-dependent states and rate-limited feedback. In the new model, the state sequence is dependent on the action sequence which is selected according to the message, and a secure rate-limited feedback link is shared between the transmitter and the receiver. We obtain the capacity-equivocation region and secrecy capacity of such a channel both for the case where the channel inputs depend noncausally on the state sequence and the case where they are restricted to causal dependence. We construct the capacity-achieving coding schemes utilizing Wyner's random binning, Gel'fand and Pinsker’s coding technique, and rate splitting. Furthermore, we compare our results with the existing approaches without feedback, with noiseless feedback, and without action-dependent states. The simulation results show that the secrecy capacity of our model is bigger than that of the first two existed approaches. Besides, it is also shown that, by taking actions to affect the channel states, we guarantee the data integrity of the message transmitted in the two-stage communication systems although the tolerable overhead of transmission time is brought.
In this paper, the general wiretap channel with channel state information (CSI) at the transmitter and noiseless feedback is investigated, where the feedback is from the legitimate receiver to the transmitter, and the CSI is available at the transmitter in a causal or noncausal manner. The capacity-equivocation regions are determined for this model in both causal and noncausal cases, and the results are further explained via Gaussian and binary examples. For the Gaussian model, we find that in some particular cases, the noiseless feedback performs better than Chia and El Gamal’s CSI sharing scheme, i.e., the secrecy capacity of this feedback scheme is larger than that of the CSI sharing scheme. For the degraded binary model, we find that the noiseless feedback performs no better than Chia and El Gamal’s CSI sharing scheme. However, if the cross-over probability of the wiretap channel is large enough, we show that the two schemes perform the same.