Limits of Reliable Communication with Low Probability of Detection on AWGN Channels

TL;DR

This paper establishes a fundamental square root limit on the amount of information that can be reliably transmitted with low probability of detection over AWGN channels, highlighting the trade-off between transmission rate and detectability.

Contribution

It proves a square root limit on reliable low-probability-of-detection communication over AWGN channels and characterizes conditions under which this limit is achievable.

Findings

Transmission beyond O(√n) bits leads to detection or decoding errors.

O(√n) bits can be reliably transmitted with low detection probability under certain noise conditions.

The square root law is fundamental for LPD communication over AWGN channels.

Abstract

We present a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over additive white Gaussian noise (AWGN) channels. Specifically, if the transmitter has AWGN channels to an intended receiver and a warden, both with non-zero noise power, we prove that $o(\sqrt{n})$ bits can be sent from the transmitter to the receiver in $n$ channel uses while lower-bounding $\alpha+\beta\geq1-\epsilon$ for any $\epsilon>0$, where $\alpha$ and $\beta$ respectively denote the warden's probabilities of a false alarm when the sender is not transmitting and a missed detection when the sender is transmitting. Moreover, in most practical scenarios, a lower bound on the noise power on the channel between the transmitter and the warden is known and $O(\sqrt{n})$ bits can be sent in $n$ LPD 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 at the receiver as $n\rightarrow\infty$.