Rate allocation for strategic users in Gaussian multiple access wiretap channels

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.

[1]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[2]  David Tse,et al.  Multiaccess Fading Channels-Part I: Polymatroid Structure, Optimal Resource Allocation and Throughput Capacities , 1998, IEEE Trans. Inf. Theory.

[3]  E. Tekin,et al.  On Secure Signaling for the Gaussian Multiple Access Wire-tap Channel , 2005, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005..

[4]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[5]  Randall Berry,et al.  Secure signaling games for Gaussian multiple access wiretap channels , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[6]  Ender Tekin,et al.  The General Gaussian Multiple-Access and Two-Way Wiretap Channels: Achievable Rates and Cooperative Jamming , 2007, IEEE Transactions on Information Theory.

[7]  Mohammad Reza Aref,et al.  Multiple Access Wiretap channels with strong secrecy , 2010, 2010 IEEE Information Theory Workshop.

[8]  Ender Tekin,et al.  Achievable Rates for the General Gaussian Multiple Access Wire-Tap Channel with Collective Secrecy , 2006, ArXiv.

[9]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[10]  Randall Berry,et al.  On Kelly-Type mechanisms for polymatroids , 2006 .

[11]  H. Vincent Poor,et al.  Generalized Multiple Access Channels with Confidential Messages , 2006, 2006 IEEE International Symposium on Information Theory.

[12]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[13]  Bruce Hajek,et al.  VCG-Kelly Mechanisms for Allocation of Divisible Goods: Adapting VCG Mechanisms to One-Dimensional Signals , 2006 .

[14]  John N. Tsitsiklis,et al.  Efficiency loss in a network resource allocation game: the case of elastic supply , 2005, IEEE Trans. Autom. Control..