Fundamental Limits of Communication With Low Probability of Detection

• Published in: IEEE transactions on information theory Vol. 62; no. 6; pp. 3493 - 3503
• Main Authors: Ligong Wang, Wornell, Gregory W., Lizhong Zheng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: AWGN channels; Blocking; Bulk molding compounds; Channels; Computer Science; Constants; covert communication; Criteria; Data transmission; Distributed processing; Entropy; Fisher information; Gaussian; Information Theory; information-theoretic security; Low probability of detection; Memoryless systems; Monte Carlo methods; Normal distribution; Receivers; Switches; Symbols; Transmitters; information-theoretic security; Low probability of detection; covert communication; Fisher information; covert communi-cation
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2016.2548471

This paper considers the problem of communication over a discrete memoryless channel (DMC) or an additive white Gaussian noise (AWGN) channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. In particular, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a DMC whose output distribution induced by the "off" input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum amount of information that can be transmitted under this criterion scales like the square root of the blocklength. The same is true for the AWGN channel. Exact expressions for the scaling constant are also derived.