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International Workshop on Signal Design and its Applications in Communications

Two Lower Bounds on the Secrecy Capacity of the Action-dependent Dirty Paper Wiretap Channel

Linman Yu, Zhuojun Zhuang, Zheng Ma, Bin Dai

Published Oct 1, 2019• 0 citations
Publisher

Abstract

In this paper, we study the state-dependent Gaussian wiretap channel with action encoder and noncausal state at the transmitter, which is also called the action-dependent dirty paper wiretap channel. Two lower bounds on the secrecy capacity of this model are provided, and we find that the two bounds have their advantages and disadvantages, i.e., none of the two always performs better than the other. In addition, we find that taking action on the state helps to increase the achievable secrecy rate of the dirty paper wiretap channel.

DOI
10.1109/iwsda46143.2019.8966104

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In this paper, we study the state-dependent Gaussian wiretap channel with action encoder and noncausal state at the transmitter, which is also called the action-dependent dirty paper wiretap channel. Two lower bounds on the secrecy capacity of this model are provided, and we find that the two bounds have their advantages and disadvantages, i.e., none of the two always performs better than the other. In addition, we find that taking action on the state helps to increase the achievable secrecy rate of the dirty paper wiretap channel.
The dirty paper wiretap channel, also referred to as the Gaussian wiretap channel with noncausal channel state at the transmitter, plays an important role in wireless physical layer security. In this paper, the dirty paper wiretap channel is revisited by considering actions on the channel state, i.e., the transmitter generates an action sequence that affects the formation of the channel state. Lower and upper bounds on the secrecy capacity of this model are proposed, and numerical results indicate that the actions on the state help to increase the achievable secrecy rate of the dirty paper wiretap channel. The study of this paper offers a new option for enhancing the secrecy rates of the state-dependent wiretap channel models.
The dirty paper wiretap channel, also referred to as the Gaussian wiretap channel with noncausal state at the transmitter, is revisited. First, we determine the secrecy capacity of the dirty paper wiretap channel with noiseless feedback, where the feedback channel is from the legitimate receiver to the transmitter. Next, we obtain lower and upper bounds on the secrecy capacity of the action-dependent dirty paper wiretap channel with noiseless feedback, and show that these bounds meet for a special case. Unlike the fact that action on the state helps to enhance the capacity of the dirty paper channel with feedback, numerical results of this paper indicate that it may not help to enhance the secrecy capacity of the dirty paper wiretap channel with feedback.
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.
We investigate the state-dependent Gaussian wiretap channel with noncausal channel state information at the transmitter (GWTC-N-CSIT), and explore whether three strategies (i.e., taking action on the state, legitimate receiver's channel output feedback, and combining the former two strategies together) help to enhance the secrecy capacity of the GWTC-N-CSIT. To be specific, we first determine the secrecy capacity of the GWTC-N-CSIT with noiseless feedback. Next, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with action-dependent state. Finally, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with both action-dependent state and noiseless feedback, and show that these bounds meet for a special case. Numerical results of this paper indicate that all three strategies enhance the secrecy capacity of the GWTC-N-CSIT. The study of this paper offers new options for enhancing the secrecy rates of the state-dependent wiretap channel models.
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.
Information embedding on actions is a new channel model in which a specific decoder is used to observe the actions taken by the encoder and retrieve part of the message intended for the receiver. We revisit this model and consider a different scenario where a secrecy constraint is imposed. By adding a wiretapper in the model, we aim to send the confidential message to the receiver and keep it secret from the wiretapper as much as possible. We characterize the inner and outer bounds on the capacity-equivocation region of such a channel with noncausal (and causal) channel state information. Furthermore, the lower and upper bounds on the sum secrecy capacity are also obtained. Besides, by eliminating the specific decoder, we get a new outer bound on the capacity-equivocation region of the wiretap channel with action-dependent states and prove it is tighter than the existing outer bound. A binary example is presented to illustrate the tradeoff between the sum secrecy rate and the information embedding rate under the secrecy constraint. We find that the secrecy constraint and the communication requirements of information embedding have a negative impact on improving the secrecy transmission rate of the given communication link.