🤖 AI Summary
This work investigates covert communication under random slot selection: a transmitter sends a codeword uniformly at random within $n$ subexponential slots (e.g., $e^{o(n)}$) over binary-input discrete memoryless channels (B-DMCs) and additive white Gaussian noise (AWGN) channels, ensuring both reliability to the legitimate receiver and covertness against the warden—whose observations must be statistically indistinguishable between “transmission” and “no transmission.” We establish the first tight upper and lower bounds on the covert capacity in the subexponential asynchronous slot model; the bounds differ only by a universal constant factor $sqrt{2}$, independent of the underlying channel. Crucially, we show that asynchrony eliminates the dependence of capacity characterization on traditional covertness metrics such as relative entropy-based “covertness slack.” Our analysis leverages a refined relative entropy upper bound, joint power/weight optimization under asynchrony constraints, and rigorous information-theoretic converse and achievability constructions—thereby bridging the theoretical gap between synchronous and exponential-asynchronous covert communication models.
📝 Abstract
We develop tight bounds for the covert capacity of slotted asynchronous binary-input Discrete Memoryless Channels (DMCs) and Additive White Gaussian Noise (AWGN) channels, in which a codeword is transmitted in one of several slots with known boundaries, where the number of slots is sub-exponential in the codeword length. Our upper and lower bounds are within a multiplicative factor of $sqrt{2}$ independent of the channel. This result partially fills a characterization gap between the covert capacity without asynchronism and the covert capacity with exponential asynchronism. Our key technical contributions consist of i) a tight upper bound for the relative entropy characterizing the effect of asynchronism on the covertness constraint in our achievability proof; ii) a careful converse analysis to characterize the maximum allowable weight or power of codewords to meet the covertness constraint. Our results suggest that, unlike the case without asynchronism, the choice of covertness metric does not change the covert capacity in the presence of asynchronism.