Boulat Bash
UMass Networks Group
Computer Science
Computer Science Building, Room 140
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, the lower bound on the noise power on 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 goes to infinity. Further, we show that LPD communication on the AWGN channel allows one to send a non-zero symbol on every channel use, in contrast to what might be expected from the square root law found recently in image-based steganography.