Second-Order Asymptotics in Covert Communication.

We study the second-order asymptotics of covert communication over binary-input DMC for three different metrics of covertness. When covertness is measured in terms of the relative entropy between the channel output distributions induced with and without communication, we characterize the exact second-order asymptotics of the number of bits that can be reliably transmitted with a probability of error less than $\epsilon$ and a relative entropy less than $\delta$. When covertness is measured in terms of the variational distance between the channel output distributions or in terms of the probability of missed detection for fixed probability of false alarm, we establish the exact first-order asymptotics and bounds on the second-order asymptotics. The main conceptual contribution of this paper is to clarify how the choice of a covertness metric impacts the information-theoretic limits of the number of covert and reliable bits. The main technical contribution of the underlying results is a detailed analysis of probability of existence of a code satisfying the reliability and covert criteria.

[1]  Alfred O. Hero,et al.  Secure space-time communication , 2003, IEEE Trans. Inf. Theory.

[2]  Christian Cachin,et al.  An information-theoretic model for steganography , 2004, Inf. Comput..

[3]  Guillermo Morales-Luna,et al.  On the Existence of Perfect Stegosystems , 2005, IWDW.

[4]  Shlomo Shamai,et al.  Information Theoretic Security , 2009, Found. Trends Commun. Inf. Theory.

[5]  H. Vincent Poor,et al.  Channel Coding Rate in the Finite Blocklength Regime , 2010, IEEE Transactions on Information Theory.

[6]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[7]  Matthieu R. Bloch,et al.  Physical-Layer Security: From Information Theory to Security Engineering , 2011 .

[8]  Donald F. Towsley,et al.  Square root law for communication with low probability of detection on AWGN channels , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[9]  Gerhard Kramer,et al.  Informational divergence approximations to product distributions , 2013, 2013 13th Canadian Workshop on Information Theory.

[10]  Igal Sason,et al.  Concentration of Measure Inequalities in Information Theory, Communications, and Coding , 2012, Found. Trends Commun. Inf. Theory.

[11]  Mayank Bakshi,et al.  Reliable deniable communication: Hiding messages in noise , 2013, 2013 IEEE International Symposium on Information Theory.

[12]  Himanshu Tyagi,et al.  Strong converse for a degraded wiretap channel via active hypothesis testing , 2014, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[13]  Gerhard Kramer,et al.  Effective secrecy: Reliability, confusion and stealth , 2013, 2014 IEEE International Symposium on Information Theory.

[14]  Information Spectrum Approach to Strong Converse Theorems for Degraded Wiretap Channels , 2015, IEEE Trans. Inf. Forensics Secur..

[15]  Aydin Sezgin,et al.  Broadcasting Into the Uncertainty: Authentication and Confidentiality by Physical-Layer Processing , 2015, Proceedings of the IEEE.

[16]  Matthieu R. Bloch,et al.  Covert Communication Over Noisy Channels: A Resolvability Perspective , 2015, IEEE Transactions on Information Theory.

[17]  H. Vincent Poor,et al.  Finite-blocklength bounds for wiretap channels , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[18]  Matthieu R. Bloch,et al.  Keyless covert communication over Multiple-Access Channels , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[19]  Lizhong Zheng,et al.  Fundamental Limits of Communication With Low Probability of Detection , 2015, IEEE Transactions on Information Theory.

[20]  Ligong Wang.  Optimal throughput for covert communication over a classical-quantum channel , 2016, 2016 IEEE Information Theory Workshop (ITW).

[21]  Donald F. Towsley,et al.  Covert communication over classical-quantum channels , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[22]  Matthieu R. Bloch,et al.  Optimal covert communications using pulse-position modulation , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).