Computer Science – Information Theory
Scientific paper
2012-02-29
Computer Science
Information Theory
Scientific paper
We present a square root limit on low probability of detection (LPD) communication over additive white Gaussian noise (AWGN) channels. Specifically, if a warden has an AWGN channel to the transmitter with non-zero noise power, we prove that $o(\sqrt{n})$ bits can be sent from the transmitter to the receiver in $n$ AWGN channel uses with probability of detection by the warden less than $\epsilon$ for any $\epsilon>0$. Moreover, in most practical scenarios, a lower bound on the noise power on the warden's channel to the transmitter is known and $O(\sqrt{n})$ bits can be covertly sent in $n$ channel uses. Conversely, attempting to transmit more than $O(\sqrt{n})$ bits either results in detection by the warden with probability one or a non-zero probability of decoding error as $n\rightarrow\infty$. Further, we show that LPD communication on the AWGN channel allows one to send a non-zero symbol on \emph{every} channel use, in contrast to what might be expected from the square root law found recently in image-based steganography.
Bash Boulat A.
Goeckel Dennis
Towsley Don
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