scholarly journals New Result on the Feedback Capacity of the Action-Dependent Dirty Paper Wiretap Channel

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 929
Author(s):  
Guangfen Xie ◽  
Bin Dai
Keyword(s):  
Lower Bound ◽  
Secrecy Capacity ◽  
Hybrid Scheme ◽  
Wiretap Channel ◽  
Numerical Examples ◽  
Feedback Model ◽  
Feedback Scheme ◽  
Channel Feedback ◽  
Noiseless Feedback ◽  
State Interference

The Gaussian wiretap channel with noncausal state interference available at the transmitter, which is also called the dirty paper wiretap channel (DP-WTC), has been extensively studied in the literature. Recently, it has been shown that taking actions on the corrupted state interference of the DP-WTC (also called the action-dependent DP-WTC) helps to increase the secrecy capacity of the DP-WTC. Subsequently, it has been shown that channel feedback further increases the secrecy capacity of the action-dependent DP-WTC (AD-DP-WTC), and a sub-optimal feedback scheme is proposed for this feedback model. In this paper, a two-step hybrid scheme and a corresponding new lower bound on the secrecy capacity of the AD-DP-WTC with noiseless feedback are proposed. The proposed new lower bound is shown to be optimal (achieving the secrecy capacity) and tighter than the existing one in the literature for some cases, and the results of this paper are further explained via numerical examples.

scholarly journals Wiretap Channel with Action-Dependent States and Rate-Limited Feedback

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Xinxing Yin ◽  
Xiao Chen ◽  
Zhi Xue
Keyword(s):  
Communication Systems ◽  
Limited Feedback ◽  
The State ◽  
Secrecy Capacity ◽  
Wiretap Channel ◽  
Action Sequence ◽  
State Sequence ◽  
Coding Schemes ◽  
Rate Splitting ◽  
Noiseless Feedback

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.

scholarly journals Feedback Schemes for the Action-Dependent Wiretap Channel with Noncausal State at the Transmitter

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 278 ◽  
Author(s):  
Haonan Zhang ◽  
Linman Yu ◽  
Bin Dai
Keyword(s):  
Secret Key ◽  
Wiretap Channel ◽  
Coding Scheme ◽  
Coding Schemes ◽  
Feedback Scheme ◽  
Noiseless Feedback ◽  
Better Than

In this paper, we propose two feedback coding schemes for the action-dependent wiretap channel with noncausal state at the transmitter. The first scheme follows from the already existing secret key based feedback coding scheme for the wiretap channel. The second one follows from our recently proposed hybrid feedback scheme for the wiretap channel. We show that, for the action-dependent wiretap channel with noncausal state at the transmitter, the second feedback scheme performs better than the first one, and the capacity results of this paper are further explained via a Gaussian example, which we call the action-dependent dirty paper wiretap channel with noiseless feedback.

scholarly journals Capacity-Equivocation Regions of the DMBCs with Noiseless Feedback

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xinxing Yin ◽  
Zhi Xue ◽  
Bin Dai
Keyword(s):  
Limited Feedback ◽  
Single Letter ◽  
Broadcast Channels ◽  
The Other ◽  
Secrecy Capacity ◽  
Wiretap Channel ◽  
The Common ◽  
Noiseless Feedback ◽  
Common Message

The discrete memoryless broadcast channels (DMBCs) with noiseless feedback are studied. The entire capacity-equivocation regions of two models of the DMBCs with noiseless feedback are obtained. One is the degraded DMBCs with rate-limited feedback; the other is thelessandreversely less noisyDMBCs with causal feedback. In both models, two kinds of messages are transmitted. The common message is to be decoded by both the legitimate receiver and the eavesdropper, while the confidential message is only for the legitimate receiver. Our results generalize the secrecy capacity of the degraded wiretap channel with rate-limited feedback (Ardestanizadeh et al., 2009) and the restricted wiretap channel with noiseless feedback (Dai et al., 2012). Furthermore, we use a simpler and more intuitive deduction to get the single-letter characterization of the capacity-equivocation region, instead of relying on the recursive argument which is complex and not intuitive.

On the Inf-Sup Constant of a Triangular Spectral Method for the Stokes Equations

2016 ◽  
Vol 16 (3) ◽  
pp. 507-522 ◽  
Author(s):  
Yanhui Su ◽  
Lizhen Chen ◽  
Xianjuan Li ◽  
Chuanju Xu
Keyword(s):  
Lower Bound ◽  
Error Estimate ◽  
Spectral Method ◽  
Stokes Equations ◽  
Necessary Condition ◽  
Well Posedness ◽  
Saddle Point Problems ◽  
Numerical Examples ◽  
Lbb Condition ◽  
Optimal Lower Bound

AbstractThe Ladyženskaja–Babuška–Brezzi (LBB) condition is a necessary condition for the well-posedness of discrete saddle point problems stemming from discretizing the Stokes equations. In this paper, we prove the LBB condition and provide the (optimal) lower bound for this condition for the triangular spectral method proposed by L. Chen, J. Shen, and C. Xu in [3]. Then this lower bound is used to derive an error estimate for the pressure. Some numerical examples are provided to confirm the theoretical estimates.

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