Fundamental Limits of Communication With Low Probability of Detection

Ligong Wang (1) , Gregory W. Wornell (2) , Lizhong Zheng (2)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes
2 MIT - Massachusetts Institute of Technology

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.

Mots clés: Fisher information; Low probability of detection; covert communi-cation; information-theoretic security

Domaines: Théorie de l'information [cs.IT]

Ligong Wang, Gregory W. Wornell, Lizhong Zheng. Fundamental Limits of Communication With Low Probability of Detection. IEEE Transactions on Information Theory, 2016, 62 (6), pp.3493-3503. ⟨10.1109/TIT.2016.2548471⟩. ⟨hal-01345907⟩