A General Characterization of Sync Word for Asynchronous Communication

We study a problem of sequential frame synchronization for a frame transmitted uniformly in A slots. For a discrete memoryless channel (DMC), Chandar et al showed in [1] that the frame length N must scale with A as e > A for the frame synchronization error to go to zero (asymptotically with A). Here, Q denotes the transition probabilities of the DMC and α(Q), defined as the synchronization threshold, characterizes the scaling needed of N for asymptotic error free frame synchronization. We show that the asynchronous communication framework permits a natural tradeoff between the sync frame length N and the channel (usually parameterised by the input). For an AWGN channel, we study this tradeoff between the sync frame length N and the input symbol power P and characterise the scaling needed of the sync frame energy E = NP for optimal frame synchronisation.