Covert Communication in the Presence of an Uninformed Jammer

By Tamara V. Sobers, Boulat A. Bash, Saikat Guha, D. Towsley, Dennis L. Goeckel. IEEE Transactions on Wireless Communications, 2016

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Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(\sqrt {n})$ </tex-math></inline-formula> bits in <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> channel uses. However, this assumes that Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>, thus conveying <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(n)$ </tex-math></inline-formula> bits covertly and reliably in <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> uses of an AWGN channel. Here, we consider covert communication of <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(n)$ </tex-math></inline-formula> bits in <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> channel uses while generalizing the environment and removing any restrictions on Willie’s receiver. We assume that an uninformed “jammer” is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie’s optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> even when Willie employs an optimal detector.

View Paper: https://www.semanticscholar.org/paper/e8f611c3e1dce592943c884d8ec1261060084165

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