Finite State Markov Wiretap Channel With Delayed Feedback

The finite-state Markov channel (FSMC), where the channel transition probability is controlled by a state undergoing a Markov process, is a useful model for the mobile wireless communication channel. In this paper, we investigate the security issue in the mobile wireless communication systems by considering the FSMC with an eavesdropper, which we call the finite-state Markov wiretap channel (FSM-WC). We assume that the state is perfectly known by the legitimate receiver and the eavesdropper, and through a noiseless feedback channel, the legitimate receiver sends his received channel output and the state back to the transmitter after some time delay. Inner and outer bounds on the capacity-equivocation regions of the FSM-WC with delayed state feedback and with or without delayed channel output feedback are provided in this paper, and we show that these bounds meet if the eavesdropper’s received symbol is a degraded version of the legitimate receiver’s. The above-mentioned results are further explained via a degraded Gaussian fading example.

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

[2]  Moritz Wiese,et al.  An achievable region for the Wiretap multiple-access channel with common message , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[3]  Giacomo Como,et al.  On the Capacity of Memoryless Finite-State Multiple-Access Channels With Asymmetric State Information at the Encoders , 2011, IEEE Transactions on Information Theory.

[4]  Sennur Ulukus,et al.  Secrecy in Cooperative Relay Broadcast Channels , 2008, IEEE Transactions on Information Theory.

[5]  Shlomo Shamai,et al.  Capacity of Cognitive Interference Channels With and Without Secrecy , 2009, IEEE Transactions on Information Theory.

[6]  Hong Shen Wang,et al.  Finite-state Markov channel-a useful model for radio communication channels , 1995 .

[7]  J. N. Laneman,et al.  On the secrecy capacity of arbitrary wiretap channels , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[8]  Bin Dai,et al.  Multiple-Access Relay Wiretap Channel , 2014, IEEE Transactions on Information Forensics and Security.

[9]  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.

[10]  Shlomo Shamai,et al.  Secret Writing on Dirty Paper: A Deterministic View , 2012, IEEE Trans. Inf. Theory.

[11]  Giacomo Como,et al.  On the capacity of finite state multiple access channels with asymmetric partial state feedback , 2009, 2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks.

[12]  Pravin Varaiya,et al.  Capacity, mutual information, and coding for finite-state Markov channels , 1996, IEEE Trans. Inf. Theory.

[13]  Pravin Varaiya,et al.  Capacity of fading channels with channel side information , 1997, IEEE Trans. Inf. Theory.

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

[15]  Jin Xu,et al.  Capacity Bounds for Broadcast Channels With Confidential Messages , 2009, IEEE Transactions on Information Theory.

[16]  Ender Tekin,et al.  The Gaussian Multiple Access Wire-Tap Channel , 2006, IEEE Transactions on Information Theory.

[17]  Bin Dai,et al.  Wiretap Channel With Side Information , 2006, ArXiv.

[18]  Andrea J. Goldsmith,et al.  Finite State Channels With Time-Invariant Deterministic Feedback , 2006, IEEE Transactions on Information Theory.

[19]  Abbas El Gamal,et al.  Wiretap Channel With Causal State Information , 2012, IEEE Transactions on Information Theory.

[20]  H. Vincent Poor,et al.  Interference Assisted Secret Communication , 2008, IEEE Transactions on Information Theory.

[21]  Imre Csiszár,et al.  Broadcast channels with confidential messages , 1978, IEEE Trans. Inf. Theory.

[22]  Zhiguo Ding,et al.  Rate Regions for Multiple Access Channel With Conference and Secrecy Constraints , 2013, IEEE Transactions on Information Forensics and Security.

[23]  Toby Berger,et al.  The capacity of finite-State Markov Channels With feedback , 2005, IEEE Transactions on Information Theory.

[24]  Abbas El Gamal,et al.  Capacity theorems for the relay channel , 1979, IEEE Trans. Inf. Theory.

[25]  Harish Viswanathan.  Capacity of Markov Channels with Receiver CSI and Delayed Feedback , 1999, IEEE Trans. Inf. Theory.

[26]  Shlomo Shamai,et al.  Secure Communication Over Fading Channels , 2007, IEEE Transactions on Information Theory.

[27]  Cyril Leung,et al.  An achievable rate region for the multiple-access channel with feedback , 1981, IEEE Trans. Inf. Theory.

[28]  Bin Dai,et al.  Feedback Enhances the Security of State-Dependent Degraded Broadcast Channels With Confidential Messages , 2015, IEEE Transactions on Information Forensics and Security.

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

[30]  Israel Bar-David,et al.  Capacity and coding for the Gilbert-Elliot channels , 1989, IEEE Trans. Inf. Theory.

[31]  Rudolf Ahlswede,et al.  General Theory of Information Transfer and Combinatorics , 2006, GTIT-C.

[32]  H. Vincent Poor,et al.  Multiple-Access Channels With Confidential Messages , 2008, IEEE Transactions on Information Theory.

[33]  Luc Vandendorpe,et al.  Multiaccess Channel With Partially Cooperating Encoders and Security Constraints , 2012, IEEE Transactions on Information Forensics and Security.

[34]  Hesham El Gamal,et al.  The Relay–Eavesdropper Channel: Cooperation for Secrecy , 2006, IEEE Transactions on Information Theory.

[35]  Yasutada Oohama,et al.  Coding for relay channels with confidential messages , 2001, Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494).

[36]  Rudolf Ahlswede,et al.  Transmission, Identification and Common Randomness Capacities for Wire-Tape Channels with Secure Feedback from the Decoder , 2006, GTIT-C.

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

[38]  Shlomo Shamai,et al.  Secret Writing on Dirty Paper: A Deterministic View , 2012, IEEE Transactions on Information Theory.

[39]  Saleem A. Kassam,et al.  Finite-state Markov model for Rayleigh fading channels , 1999, IEEE Trans. Commun..

[40]  Andrew Thangaraj,et al.  Finite-state wiretap channels: Secrecy under memory constraints , 2009, 2009 IEEE Information Theory Workshop.

[41]  Bin Dai,et al.  Relay Broadcast Channel With Confidential Messages , 2016, IEEE Transactions on Information Forensics and Security.

[42]  Haim H. Permuter,et al.  Capacity Region of Finite State Multiple-Access Channels With Delayed State Information at the Transmitters , 2011, IEEE Transactions on Information Theory.

[43]  Haim H. Permuter,et al.  Capacity Region of the Finite-State Multiple-Access Channel With and Without Feedback , 2007, IEEE Transactions on Information Theory.

[44]  Roy D. Yates,et al.  Discrete Memoryless Interference and Broadcast Channels With Confidential Messages: Secrecy Rate Regions , 2007, IEEE Transactions on Information Theory.