Percolation on the information theoretic secure SINR graph: Upper and lower bounds

Connectivity in an information-theoretically secure graph is considered where both the legitimate and the eavesdropper nodes are distributed as Poisson point processes. To allow concurrent transmissions from multiple legitimate nodes, a signal-to-interference plus noise ratio secure graph is introduced, and its percolation (having an unbounded connected component) properties are studied. It is shown that for a fixed eavesdropper node density, percolation happens for large enough (but finite) legitimate node density and small enough interference suppression parameter of the legitimate nodes. Conversely, a concrete bound is obtained that shows that if the legitimate node density is below a fixed threshold, then the probability of percolation is zero.

[1]  M. Penrose.  On a continuum percolation model , 1991, Advances in Applied Probability.

[2]  Rahul Vaze.  Percolation and connectivity on the signal to interference ratio graph , 2012, 2012 Proceedings IEEE INFOCOM.

[3]  Onur Ozan Koyluoglu,et al.  On Secrecy Capacity Scaling in Wireless Networks , 2012, IEEE Transactions on Information Theory.

[4]  Kin K. Leung,et al.  Artificial Noise Generation from Cooperative Relays for Everlasting Secrecy in Two-Hop Wireless Networks , 2011, IEEE Journal on Selected Areas in Communications.

[5]  Martin Haenggi,et al.  Secrecy coverage , 2010, 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers.

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

[7]  R. Durrett.  Probability: Theory and Examples , 1993 .

[8]  Mathew D. Penrose,et al.  Random Geometric Graphs , 2003 .

[9]  P. Thiran,et al.  Percolation in the signal to interference ratio graph , 2006, Journal of Applied Probability.

[10]  Martin Haenggi.  The secrecy graph and some of its properties , 2008, 2008 IEEE International Symposium on Information Theory.

[11]  Matthieu R. Bloch,et al.  Wireless Information-Theoretic Security , 2008, IEEE Transactions on Information Theory.

[12]  Martin E. Hellman,et al.  The Gaussian wire-tap channel , 1978, IEEE Trans. Inf. Theory.

[13]  Moe Z. Win,et al.  Percolation and Connectivity in the Intrinsically Secure Communications Graph , 2012, IEEE Transactions on Information Theory.

[14]  François Baccelli,et al.  Impact of interferences on connectivity in ad hoc networks , 2005, IEEE/ACM Transactions on Networking.

[15]  Donald F. Towsley,et al.  Physical layer security from inter-session interference in large wireless networks , 2012, 2012 Proceedings IEEE INFOCOM.

[16]  Isaac Balberg.  Continuum Percolation , 2009, Encyclopedia of Complexity and Systems Science.

[17]  A. Robert Calderbank,et al.  The Effect of Eavesdroppers on Network Connectivity: A Secrecy Graph Approach , 2011, IEEE Transactions on Information Forensics and Security.

[18]  Massimo Franceschetti,et al.  Closing the gap in the capacity of random wireless networks , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[19]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[20]  Piyush Gupta,et al.  Critical Power for Asymptotic Connectivity in Wireless Networks , 1999 .

[21]  Jean-Baptiste Gouéré,et al.  Existence of subcritical regimes in the Poisson Boolean model of continuum percolation , 2006, math/0611369.

[22]  Martin Haenggi,et al.  Percolation in the secrecy graph , 2013, Discret. Appl. Math..

[23]  E. N. Gilbert,et al.  Random Plane Networks , 1961 .

[24]  David Tse,et al.  Mobility increases the capacity of ad hoc wireless networks , 2002, TNET.

[25]  Martin Haenggi,et al.  Percolation in the secrecy graph , 2011, 2011 Information Theory and Applications Workshop.

[26]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .