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Covert Identification over Binary-Input Discrete Memoryless Channels. (arXiv:2007.13333v2 [cs.IT] UPDATED)

This paper considers the covert identification problem in which a sender aims
to reliably convey an identification (ID) message to a set of receivers via a
binary-input discrete memoryless channel (BDMC), and simultaneously to
guarantee that the communication is covert with respect to a warden who
monitors the communication via another independent BDMC. We prove a square-root
law for the covert identification problem. This states that an ID message of
size exp(exp(Theta(sqrt{n}))) can be transmitted over n channel uses. We
then characterize the exact pre-constant in the Theta(.) notation. This
constant is referred to as the covert identification capacity. We show that it
equals the recently developed covert capacity in the standard covert
communication problem, and somewhat surprisingly, the covert identification
capacity can be achieved without any shared key between the sender and
receivers. The achievability proof relies on a random coding argument with
pulse-position modulation (PPM), coupled with a second stage which performs
code refinements. The converse proof relies on an expurgation argument as well
as results for channel resolvability with stringent input constraints.