Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

Secure signaling games for Gaussian multiple access wiretap channels

Hao Ge, Ruijie Xu, Randall Berry

Published Jun 1, 2015• 11 citations
Publisher

Abstract

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.

DOI
10.1109/isit.2015.7282427

Related papers

On Secure Signaling for the Gaussian Multiple Access Wire-tap Channel

Ender Tekin, Semih Serbetli, Aylin Yener

Abstract — We consider the Gaussian Multiple Access Wire-Tap Channel (GMAC-WT) where multiple users communicate with the intended receiver in the presence of an intelligent and informed wire-tapper (eavesdropper). The wire-tapper receives a degraded version of the signal at the receiver. We assume that the wire-tapper is as capable as the intended receiver, and there is no other shared secret key. We consider two different secure communication scenarios: (i) keeping the wire-tapper totally ignorant of the message of any group of users even if the remaining users are compromised, (ii) using the secrecy of the other users to ensure secrecy for a group of users. We first derive the outer bounds for the secure rate region. Next, using Gaussian codebooks, we show the achievability of a secure rate region for each measure in which the wire-tapper is kept perfectly ignorant of the messages. We also find the power allocations that yield the maximum sum rate, and show that upper bound on the secure sum rate can be achieved by a TDMA scheme. 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. I.

Asilomar Conference on Signals, Systems and Computers (ACSSC)•Mar 22, 2006•51 citations

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

Ender Tekin, Aylin Yener

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.

arXiv:cs/0702051•Information Theory and Applications Workshop (ITA)•Jan 1, 2007•51 citations

Some New Results on the Multiple-AccessWiretap Channel

Bin Dai, Zheng Ma

In this paper, some new results on the multiple-access wiretap channel (MAC-WT) are provided. Specifically, first, we investigate the degraded MAC-WT, where two users transmit their corresponding confidential messages (no common message) to a legitimate receiver via a multiple-access channel (MAC), while a wiretapper wishes to obtain the messages via a physically degraded wiretap channel. The secrecy capacity region of this model is determined for both the discrete memoryless and Gaussian cases. For the Gaussian case, we find that this secrecy capacity region is exactly the same as the achievable secrecy rate region provided by Tekin and Yener, i.e., Tekin–Yener’s achievable region is exactly the secrecy capacity region of the degraded Gaussian MAC-WT. Second, we study a special Gaussian MAC-WT, and find the power control for two kinds of optimal points (max-min point and single user point) on the secrecy rate region of this special Gaussian model.

Entropy•Aug 21, 2014•5 citations

Resource allocation in fading multiple access wiretap channel via game theoretic learning

Shahid Mehraj Shah, Atmakuri Krishna Chaitanya, Vinod Sharma

In this paper we consider a K-user fading multiple access wiretap channel, where each user wants to transmit a message confidentially. There is a passive eavesdropper (Eve) at the receiving end. We are interested in allocating rates and powers to the users fairly and reliably without the eavesdropper being able to decode the message. Initially we assume that each user knows only its own channel gain to the receiver and to the eavesdropper. When any user transmits a message, the receiver send an ACK if the message is decoded correctly and confidentially, else it sends a NACK. We use Multiplicative Weight no-regret algorithm to obtain a coarse correlated equilibrium. Next we maximize the weighted sum of utility of all the users and obtain Pareto optimal points. Since not all Pareto points are fair, we also obtain Nash Bargaining (NB) solutions which ensure certain fairness to all the users. In the next part of the paper we make more realistic assumption that each user knows only its own channel gain, and is ignorant of the channel gain to Eve (only its distribution is known). We use secrecy outage as the metric at the receiver to decide weather the message is correctly decoded or not. We obtain a coarse correlated equilibrium, a Pareto point and a Nash bargaining solution.

Information Theory and Applications Workshop (ITA)•Jan 1, 2016•4 citations

Rate allocation for strategic users in Gaussian multiple access wiretap channels

Hao Ge, Randall Berry

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.

International Conference on Communications•May 1, 2017•3 citations

On the Secrecy Capacity Region of Multiple Access Wire-tap Channel with Common Message

Hassan ZivariFard, Bahareh Akhbari, Mahmoud Ahmadian‐Attari +1 more

In this paper, we study the problem of secret communication over a Multiple Access Wire-tap Channel with Common Message. Here, we assume that two transmitters have confidential messages which must be kept secret from the eavesdropper (the second receiver), and both of them have access to a common message which can be decoded by two receivers. For this setting, we derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case as well as for Gaussian one. Providing numerical examples for the Gaussian case, we illustrate the comparison between derived achievable rate regions and outer bounds for our considered model and the capacity region of compound multiple access channel.

arXiv:1402.4799?context=math•Feb 19, 2014•0 citations
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.
Abstract — We consider the Gaussian Multiple Access Wire-Tap Channel (GMAC-WT) where multiple users communicate with the intended receiver in the presence of an intelligent and informed wire-tapper (eavesdropper). The wire-tapper receives a degraded version of the signal at the receiver. We assume that the wire-tapper is as capable as the intended receiver, and there is no other shared secret key. We consider two different secure communication scenarios: (i) keeping the wire-tapper totally ignorant of the message of any group of users even if the remaining users are compromised, (ii) using the secrecy of the other users to ensure secrecy for a group of users. We first derive the outer bounds for the secure rate region. Next, using Gaussian codebooks, we show the achievability of a secure rate region for each measure in which the wire-tapper is kept perfectly ignorant of the messages. We also find the power allocations that yield the maximum sum rate, and show that upper bound on the secure sum rate can be achieved by a TDMA scheme. 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. I.
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.
In this paper, some new results on the multiple-access wiretap channel (MAC-WT) are provided. Specifically, first, we investigate the degraded MAC-WT, where two users transmit their corresponding confidential messages (no common message) to a legitimate receiver via a multiple-access channel (MAC), while a wiretapper wishes to obtain the messages via a physically degraded wiretap channel. The secrecy capacity region of this model is determined for both the discrete memoryless and Gaussian cases. For the Gaussian case, we find that this secrecy capacity region is exactly the same as the achievable secrecy rate region provided by Tekin and Yener, i.e., Tekin–Yener’s achievable region is exactly the secrecy capacity region of the degraded Gaussian MAC-WT. Second, we study a special Gaussian MAC-WT, and find the power control for two kinds of optimal points (max-min point and single user point) on the secrecy rate region of this special Gaussian model.
In this paper we consider a K-user fading multiple access wiretap channel, where each user wants to transmit a message confidentially. There is a passive eavesdropper (Eve) at the receiving end. We are interested in allocating rates and powers to the users fairly and reliably without the eavesdropper being able to decode the message. Initially we assume that each user knows only its own channel gain to the receiver and to the eavesdropper. When any user transmits a message, the receiver send an ACK if the message is decoded correctly and confidentially, else it sends a NACK. We use Multiplicative Weight no-regret algorithm to obtain a coarse correlated equilibrium. Next we maximize the weighted sum of utility of all the users and obtain Pareto optimal points. Since not all Pareto points are fair, we also obtain Nash Bargaining (NB) solutions which ensure certain fairness to all the users. In the next part of the paper we make more realistic assumption that each user knows only its own channel gain, and is ignorant of the channel gain to Eve (only its distribution is known). We use secrecy outage as the metric at the receiver to decide weather the message is correctly decoded or not. We obtain a coarse correlated equilibrium, a Pareto point and a Nash bargaining solution.
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.
In this paper, we study the problem of secret communication over a Multiple Access Wire-tap Channel with Common Message. Here, we assume that two transmitters have confidential messages which must be kept secret from the eavesdropper (the second receiver), and both of them have access to a common message which can be decoded by two receivers. For this setting, we derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case as well as for Gaussian one. Providing numerical examples for the Gaussian case, we illustrate the comparison between derived achievable rate regions and outer bounds for our considered model and the capacity region of compound multiple access channel.