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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(&#x221A;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 e for any &#x03F5; &gt;; 0, and, if a lower bound on the noise power on the warden's channel is known, then O(&#x221A;n) bits can be covertly sent in n channel uses. Conversely, trying to transmit more than O(&#x221A;n) bits either results in detection by the warden with probability one or a non-zero probability of decoding error as n &#x2192; &#x221E;. Further, we show that LPD communication on the AWGN channel allows one to send a nonzero symbol on every channel use, in contrast to what might be expected from the square root law found recently in image-based steganography.

Square root law for communication with low probability of detection on AWGN channels