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IEEE Transactions on Information Forensics and Security

Adding a Helper Can Totally Remove the Secrecy Constraints in a Two-User Interference Channel

Jinyuan Chen, Fan Li

Published Apr 27, 2019• 16 citations
Publisher

Abstract

In many communication channels, secrecy constraintsusuallyincur a penalty in capacity, as well as generalized degrees-of-freedom (GDoF). In this paper, we show an interesting observation that adding a helper cantotallyremove the penalty in sum GDoF for a two-user symmetric Gaussian interference channel. For the interference channel where each transmitter sends a message to an intended receiver without secrecy constraints, the sum GDoF is a well-known “W” curve, characterized by Etkin–Tse–Wang in 2008. If the secrecy constraints are imposed on this interference channel, where the message of each transmitter must be secure from the unintended receiver (eavesdropper), then a GDoF penalty is incurred and the secure sum GDoF is reduced to a modified “W” curve, derived by Chen recently. In this paper, we show that, by adding a helper into this interference channel with secrecy constraints, thesecuresum GDoF turns out to be a “W” curve, which is the same as the sum GDoF of the setting without secrecy constraints. The proposed scheme is based on the cooperative jamming and a careful signal design such that the jamming signal of the helper is aligned at a specific direction and power level with the information signals of the transmitters, which allows us to totally remove the penalty in GDoF due to the secrecy constraints. Furthermore, the estimation approaches of noise removal and signal separation due to the rational independence are used in the secure rate analysis.

DOI
10.1109/tifs.2019.2913514

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In this paper, the role of unidirectional limited rate transmitter cooperation is studied for the two-user symmetric Z interference channel (Z-IC) with secrecy constraints at the receivers, in achieving two conflicting goals simultaneously: mitigating interference and ensuring secrecy. First, the problem is studied under the linear deterministic model. A novel scheme for partitioning the encoded messages and outputs based on the relative strengths of the signal and interference is proposed. The partitioning reveals the side information that needs to be provided to the receiver and facilitates the development of tight outer bounds on the secrecy capacity region. The achievable schemes for the deterministic model use a fusion of cooperative precoding and transmission of a jamming signal. The optimality of the proposed scheme is established for the deterministic model for all possible parameter settings. The insights obtained from the deterministic model are used to derive inner and outer bounds on the secrecy capacity region of the two-user Gaussian symmetric Z-IC. The achievable scheme for the Gaussian model uses stochastic encoding in addition to cooperative precoding and transmission of a jamming signal. For the Gaussian case, the secure sum generalized degrees of freedom (GDOF) is characterized and shown to be optimal for the weak/moderate interference regime. It is also shown that the secure sum capacity lies within 2 bits/s/Hz of the outer bound for the weak/moderate interference regime for all values of the capacity of the cooperative link. Interestingly, in the deterministic model, it is found that there is no penalty on the capacity region of the Z-IC due to the secrecy constraints at the receivers in the weak/moderate interference regimes. Similarly, it is found that there is no loss in the secure sum GDOF for the Gaussian case due to the secrecy constraint at the receiver, in the weak/moderate interference regimes. The results highlight the importance of cooperation in facilitating secure communication over the Z-IC.

IEEE Transactions on Information Forensics and Security•Oct 26, 2016•10 citations
In many communication channels, secrecy constraintsusuallyincur a penalty in capacity, as well as generalized degrees-of-freedom (GDoF). In this paper, we show an interesting observation that adding a helper cantotallyremove the penalty in sum GDoF for a two-user symmetric Gaussian interference channel. For the interference channel where each transmitter sends a message to an intended receiver without secrecy constraints, the sum GDoF is a well-known “W” curve, characterized by Etkin–Tse–Wang in 2008. If the secrecy constraints are imposed on this interference channel, where the message of each transmitter must be secure from the unintended receiver (eavesdropper), then a GDoF penalty is incurred and the secure sum GDoF is reduced to a modified “W” curve, derived by Chen recently. In this paper, we show that, by adding a helper into this interference channel with secrecy constraints, thesecuresum GDoF turns out to be a “W” curve, which is the same as the sum GDoF of the setting without secrecy constraints. The proposed scheme is based on the cooperative jamming and a careful signal design such that the jamming signal of the helper is aligned at a specific direction and power level with the information signals of the transmitters, which allows us to totally remove the penalty in GDoF due to the secrecy constraints. Furthermore, the estimation approaches of noise removal and signal separation due to the rational independence are used in the secure rate analysis.
In many communication channels, secrecy constraints usually incur a penalty in capacity, as well as generalized degrees-of-freedom (GDoF). In this work we show an interesting observation that, adding a helper can totally remove the penalty in sum GDoF, for a two-user symmetric Gaussian interference channel. For the interference channel where each transmitter sends a message to an intended receiver without secrecy constraints, the sum GDoF is a well-known "W" curve, characterized by Etkin-Tse-Wang in 2008. If the secrecy constraints are imposed on this interference channel, where the message of each transmitter must be secure from the unintended receiver (eavesdropper), then a GDoF penalty is incurred and the secure sum GDoF is reduced to a modified "W" curve, derived by Chen recently. In this work we show that, by adding a helper into this interference channel with secrecy constraints, the secure sum GDoF turns out to be a "W" curve, which is the same as the sum GDoF of the setting without secrecy constraints. The proposed scheme is based on the cooperative jamming and a careful signal design such that the jamming signal of the helper is aligned at a specific direction and power level with the information signals of the transmitters, which allows to totally remove the penalty in GDoF due to the secrecy constraints. Furthermore, the estimation approaches of noise removal and signal separation due to the rational independence are used in the secure rate analysis.
We study a symmetric Gaussian wiretap channel with a helper, where a confidential message is sent from a transmitter to a legitimate receiver, in the presence of a helper and an eavesdropper, under a weak notion of secrecy constraint. For this setting, we characterize the optimal secure generalized degrees-of-freedom (GDoF). The result reveals that, adding a helper can significantly increase the secure GDoF of the wiretap channel. The result is supported by a new converse and a new scheme. In the proposed scheme, the helper sends a cooperative jamming signal at a specific power level and direction. In this way, it minimizes the penalty in GDoF incurred by the secrecy constraint. In the secure rate analysis, the techniques of noise removal and signal separation are used.
We study a symmetric Gaussian wiretap channel with a helper, where a confidential message is sent from a transmitter to a legitimate receiver, in the presence of a helper and an eavesdropper, under a weak notion of secrecy constraint. For this setting, we characterize the optimal secure generalized degrees-of-freedom (GDoF). The result reveals that, adding a helper can significantly increase the secure GDoF of the wiretap channel. The result is supported by a new converse and a new scheme. In the proposed scheme, the helper sends a cooperative jamming signal at a specific power level and direction. In this way, it minimizes the penalty in GDoF incurred by the secrecy constraint. In the secure rate analysis, the techniques of noise removal and signal separation are used.
We study a symmetric Gaussian wiretap channel with a helper, where a confidential message is sent from a transmitter to a legitimate receiver, in the presence of a helper and an eavesdropper. For this setting, we characterize the optimal secure generalized degrees-of-freedom (GDoF). The result reveals that, adding a helper can significantly increase the secure GDoF of the wiretap channel. The result is supported by a new converse and a new scheme. In the proposed scheme, the helper sends a cooperative jamming signal at a specific power level and direction. In this way, it minimizes the penalty in GDoF incurred by the secrecy constraint. In the secure rate analysis, the techniques of noise removal and signal separation are used.
In communication networks secrecy constraints usually incur an extra limit in capacity or generalized degrees-of-freedom (GDoF), in the sense that a penalty in capacity or GDoF is incurred due to the secrecy constraints. Over the past decades a significant amount of effort has been made by the researchers to understand the limits of secrecy constraints in communication networks. In this work, we focus on how to remove the secrecy penalty in communication networks, i.e., how to remove the GDoF penalty due to secrecy constraints. We begin with three basic settings: a two-user symmetric Gaussian interference channel with confidential messages, a symmetric Gaussian wiretap channel with a helper, and a two-user symmetric Gaussian multiple access wiretap channel. Interestingly, in this work we show that adding common randomness at the transmitters can totally remove the penalty in GDoF or GDoF region of the three settings considered here. The results reveal that adding common randomness at the transmitters is a powerful way to remove the secrecy penalty in communication networks in terms of GDoF performance. Common randomness can be generated offline before the real-time message communication. The role of the common randomness is to jam the information signal at the eavesdroppers, without causing too much interference at the legitimate receivers. To accomplish this role, a new method of Markov chain-based interference neutralization is proposed in the achievability schemes utilizing common randomness. From the practical point of view, we need to minimize the amount of common randomness used for removing the secrecy penalty in terms of GDoF performance. With this motivation, for most of the cases we characterize the minimal GDoF of common randomness to remove secrecy penalty, based on our derived converses and achievability.
In this paper, the role of unidirectional limited rate transmitter cooperation is studied for the two-user symmetric Z interference channel (Z-IC) with secrecy constraints at the receivers, in achieving two conflicting goals simultaneously: mitigating interference and ensuring secrecy. First, the problem is studied under the linear deterministic model. A novel scheme for partitioning the encoded messages and outputs based on the relative strengths of the signal and interference is proposed. The partitioning reveals the side information that needs to be provided to the receiver and facilitates the development of tight outer bounds on the secrecy capacity region. The achievable schemes for the deterministic model use a fusion of cooperative precoding and transmission of a jamming signal. The optimality of the proposed scheme is established for the deterministic model for all possible parameter settings. The insights obtained from the deterministic model are used to derive inner and outer bounds on the secrecy capacity region of the two-user Gaussian symmetric Z-IC. The achievable scheme for the Gaussian model uses stochastic encoding in addition to cooperative precoding and transmission of a jamming signal. For the Gaussian case, the secure sum generalized degrees of freedom (GDOF) is characterized and shown to be optimal for the weak/moderate interference regime. It is also shown that the secure sum capacity lies within 2 bits/s/Hz of the outer bound for the weak/moderate interference regime for all values of the capacity of the cooperative link. Interestingly, in the deterministic model, it is found that there is no penalty on the capacity region of the Z-IC due to the secrecy constraints at the receivers in the weak/moderate interference regimes. Similarly, it is found that there is no loss in the secure sum GDOF for the Gaussian case due to the secrecy constraint at the receiver, in the weak/moderate interference regimes. The results highlight the importance of cooperation in facilitating secure communication over the Z-IC.