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IEEE International Symposium on Information Theory (ISIT)

The degraded Gaussian multiple access wiretap channel with selfish transmitters: A coalitional game theory perspective

Rémi A. Chou, Aylin Yener

Published Jun 1, 2017• 4 citations
Publisher

Abstract

We study the degraded Gaussian multiple access wiretap channel with selfish transmitters, i.e., they are each solely interested in maximizing their individual secrecy rate. The question then arises as to whether selfish transmitters can increase their individual secrecy rate by participating in a collective, i.e, multiple access, protocol instead of operating on their own. If yes, the question arises if there is a protocol that satisfies all the participating transmitters, in the sense that no transmitter has an incentive to deviate from the protocol. We answer these questions in the positive utilizing coalitional game theory. In particular, we show that cooperation is in the best interest of all transmitters and that there exist protocols that incentivize all transmitters to participate. Furthermore, we determine a unique, fair, and stable achievable secrecy rate allocation.

DOI
10.1109/isit.2017.8006820

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The Gaussian Multiple Access Wiretap Channel With Selfish Transmitters: A Coalitional Game Theory Perspective

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This paper considers the Gaussian multiple access wiretap channel (GMAC-WT) with selfish transmitters, i.e., who are each solely interested in maximizing their individual secrecy rate. The question then arises as to whether selfish transmitters can increase their individual secrecy rate by participating in a collective, i.e, multiple access, protocol instead of operating on their own. If yes, the question arises whether there is a protocol that satisfies all the participating transmitters simultaneously, in the sense that no transmitter has an incentive to deviate from the protocol. Utilizing coalitional game theory, these questions are addressed for the degraded GMAC-WT with an arbitrary number of transmitters and for the non-degraded GMAC-WT with two transmitters. In particular, for the degraded GMAC-WT, cooperation is shown to be in the best interest of all transmitters, and the existence of protocols that incentivize all transmitters to participate is established. Furthermore, a unique, fair, stable, and achievable secrecy rate allocation is determined. For the non-degraded GMAC-WT, depending on the channel parameters, there are cases where cooperation is not in the best interest of all transmitters, and cases where it is. In the latter cases, a unique, fair, stable, and achievable secrecy rate allocation is determined.

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The Gaussian multiple access wire-tap channel: wireless secrecy and cooperative jamming

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We consider the General Gaussian Multiple Access Wire-Tap Channel (GGMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed eavesdropper. We define two suitable secrecy measures, termed individual and collective, to reflect the confidence in the system for this multi-access environment. We determine achievable rates such that secrecy to some pre-determined degree can be maintained, using Gaussian codebooks. We also find outer bounds for the case when the eavesdropper receives a degraded version of the intended receiver's signal. In the degraded case, Gaussian codewords are shown to achieve the sum capacity for collective constraints. In addition, a TDMA scheme is shown to also achieve sum capacity for both sets of constraints. Numerical results showing the new rate region are presented and compared with the capacity region of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints. We then find the secrecy sum-rate maximizing power allocations for the transmitters, and show that a cooperative jamming scheme can be used to increase achievable rates in this scenario.

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Ender Tekin, Aylin Yener

The general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy ldquojamrdquo the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system.

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Secure signaling games for Gaussian multiple access wiretap channels

Hao Ge, Ruijie Xu, Randall Berry

A Gaussian multiple access wire-tap channel with confidential messages is studied, where multiple users attempt to transmit private messages to a legitimate receiver in the presence of an eavesdropper. While prior work focused on the case where the users were cooperative, we assume that each user is selfish and and so are modeled as playing a non-cooperative game. We assume all users send a superposition of two Gaussian codebooks: one for their confidential messages and one for “filling” the evesdropper's channel. For such a scheme, we give a characterization of the achievable rate region defined by Tekin and Yener using polymatroid properties. We then use this to find the Nash equilibrium region for this non-cooperative game. Furthermore, we give algorithms for finding the best and worst Nash equilibria for a given channel.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2015•11 citations
We study the degraded Gaussian multiple access wiretap channel with selfish transmitters, i.e., they are each solely interested in maximizing their individual secrecy rate. The question then arises as to whether selfish transmitters can increase their individual secrecy rate by participating in a collective, i.e, multiple access, protocol instead of operating on their own. If yes, the question arises if there is a protocol that satisfies all the participating transmitters, in the sense that no transmitter has an incentive to deviate from the protocol. We answer these questions in the positive utilizing coalitional game theory. In particular, we show that cooperation is in the best interest of all transmitters and that there exist protocols that incentivize all transmitters to participate. Furthermore, we determine a unique, fair, and stable achievable secrecy rate allocation.
This paper considers the Gaussian multiple access wiretap channel (GMAC-WT) with selfish transmitters, i.e., who are each solely interested in maximizing their individual secrecy rate. The question then arises as to whether selfish transmitters can increase their individual secrecy rate by participating in a collective, i.e, multiple access, protocol instead of operating on their own. If yes, the question arises whether there is a protocol that satisfies all the participating transmitters simultaneously, in the sense that no transmitter has an incentive to deviate from the protocol. Utilizing coalitional game theory, these questions are addressed for the degraded GMAC-WT with an arbitrary number of transmitters and for the non-degraded GMAC-WT with two transmitters. In particular, for the degraded GMAC-WT, cooperation is shown to be in the best interest of all transmitters, and the existence of protocols that incentivize all transmitters to participate is established. Furthermore, a unique, fair, stable, and achievable secrecy rate allocation is determined. For the non-degraded GMAC-WT, depending on the channel parameters, there are cases where cooperation is not in the best interest of all transmitters, and cases where it is. In the latter cases, a unique, fair, stable, and achievable secrecy rate allocation is determined.
We consider the General Gaussian Multiple Access Wire-Tap Channel (GGMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed eavesdropper. We define two suitable secrecy measures, termed individual and collective, to reflect the confidence in the system for this multi-access environment. We determine achievable rates such that secrecy to some pre-determined degree can be maintained, using Gaussian codebooks. We also find outer bounds for the case when the eavesdropper receives a degraded version of the intended receiver's signal. In the degraded case, Gaussian codewords are shown to achieve the sum capacity for collective constraints. In addition, a TDMA scheme is shown to also achieve sum capacity for both sets of constraints. Numerical results showing the new rate region are presented and compared with the capacity region of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints. We then find the secrecy sum-rate maximizing power allocations for the transmitters, and show that a cooperative jamming scheme can be used to increase achievable rates in this scenario.
The general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy ldquojamrdquo the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system.
We consider a set of users communicating over a Gaussian multiple access channel in the presence of an eavesdropper. The information theoretic secrecy rates for such settings have been well studied under the assumptions that all users are cooperative. In more recent work, a game theoretic model was studied in which each user selected its own rate. This game was shown to have multiple possible equilibria. Here, we consider a related question in which a mechanism is used to solicit information from the users and then allocate secrecy rates among them. We study three simple mechanisms and analyze the performance of each for a small set of users (N = 2, 3) in terms of their worst-case efficiency. For N = 2, we give a closed form lower bound on the efficiency for each scheme and show one mechanism, which generalizes the well-known Kelly mechanism, has the best efficiency. We then consider N = 3 users and give numerical results for different user utility functions.
We consider the General Gaussian Multiple Access Wire-Tap Channel (GGMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed eavesdropper who is as capable as the intended receiver, but has different channel parameters. We aim to provide perfect secrecy for the transmitters in this multi-access environment. Using Gaussian codebooks, an achievable secrecy region is determined and the power allocation that maximizes the achievable sum-rate is found. Numerical results showing the new rate region are presented. It is shown that the multiple-access nature of the channel may be utilized to allow users with zero single-user secrecy capacity to be able to transmit in perfect secrecy. In addition, a new collaborative scheme is shown that may increase the achievable sum-rate. In this scheme, a user who would not transmit to maximize the sum rate can help another user who (i) has positive secrecy capacity to increase its rate, or (ii) has zero secrecy capacity to achieve a positive secrecy capacity.
A Gaussian multiple access wire-tap channel with confidential messages is studied, where multiple users attempt to transmit private messages to a legitimate receiver in the presence of an eavesdropper. While prior work focused on the case where the users were cooperative, we assume that each user is selfish and and so are modeled as playing a non-cooperative game. We assume all users send a superposition of two Gaussian codebooks: one for their confidential messages and one for “filling” the evesdropper's channel. For such a scheme, we give a characterization of the achievable rate region defined by Tekin and Yener using polymatroid properties. We then use this to find the Nash equilibrium region for this non-cooperative game. Furthermore, we give algorithms for finding the best and worst Nash equilibria for a given channel.