On sequential frame synchronization with clock misalignment

We study one shot frame synchronization in a discrete memoryless channel where, a sync frame of known length Nv symbols is transmitted at a random time v. For a random misalignment 7 between the transmitter clock and the receiver clock, we seek to characterize the sync frame (length) necessary for error-free frame synchronization. We assume that the random times v and 7 are independent and have a general distribution. Using a variable length sync word and a multi-stage sequential decoder for the setup, we derive necessary and sufficient scaling of the average sync frame length for asymptotic error-free frame synchronization. In particular, we show that the average sync frame length must scale with the entropy of v and/or logarithm of cardinality of the sample space of 7. We illustrate our results for the AWGN channel and also derive the scaling needed of the sync frame energy for the asynchronous setup.