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arXiv:2406.04521 · IEEE Transactions on Information Theory

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

Rémi A. Chou, Aylin Yener

Published Jun 10, 2024• 0 citations
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Abstract

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.

DOI
10.1109/tit.2024.3411918

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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.
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.
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 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.
We consider the Gaussian multiple access wire-tap channel (GMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed wire-tapper who receives a degraded version of the signal at the receiver. We define a suitable security measure for this multi-access environment. We derive an outer bound for the rate region such that secrecy to some pre-determined degree can be maintained. We also find, using Gaussian codebooks, an achievable such secrecy region. Gaussian codewords are shown to achieve the sum capacity outer bound, and the achievable region coincides with the outer bound for Gaussian codewords, giving the capacity region when inputs are constrained to be Gaussian. We present numerical results showing the new rate region and compare it with that of the Gaussian multiple-access channel (GMAC) with no secrecy constraints
In this paper, we study the two transmitter multiple-access channel (MAC) with noncausal side information at one (single-sided) or both (two-sided) of the encoders in the presence of an external wiretapper (WT) and under individual and collective secrecy constraints. Our work consists of four parts. First, we consider the discrete memoryless (DM-MAC-WT) case of the model and derive inner and outer bounds on the secrecy capacity region under both of the secrecy constraints. Second, the results are extended to the Gaussian memoryless case [Gaussian multiple-access channel WT (GMAC-WT)] in detail and are used to illustrate numerically that the secrecy rate region is enlarged by increasing the power of the interference signal which is known noncausally at the encoder. Third, we analyze the strong interference regime as an important regime in GMAC with side information and show that under collective secrecy constraint, we can achieve the secrecy capacity region of the single-sided channel asymptotically for a special case in which the signal and noise powers satisfy specific constraints. To the best of our knowledge, this capacity region is the first one obtained for GMAC-WT. Finally, we show that our results include previous works as its special cases for both the single-sided and two-sided channel models.
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.