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.