LPD communication when the warden does not know when

Unlike standard security methods (e.g. encryption), low probability of detection (LPD) communication does not merely protect the information contained in a transmission from unauthorized access, but prevents the detection of a transmission in the first place. In this work we study the impact of secretly pre-arranging the time of communication. We prove that if Alice has AWGN channels to Bob and the warden, and if she and Bob can choose a single n symbol period slot out of T(n) such slots, keeping the selection secret from the warden (and, thus, forcing him to monitor all T(n) slots), then Alice can reliably transmit O(min[√n log T(n),n]) bits to Bob while keeping the warden's detector ineffective. The result indicates that only an additional log T(n) secret bits need to be exchanged between Alice and Bpob prior to communication to produce a multiplicative gain of √log T(n) in the amount of transmitted covert information.