Abstract-We consider the "one-shot frame synchronization problem," where a decoder wants to locate a sync pattern at the output of a memoryless channel on the basis of sequential observations. The sync pattern of length N starts being emitted at a random time within some interval of size A, where A characterizes the asynchronism level. We show that a sequential decoder can optimally locate the sync pattern, i.e., exactly, without delay, and with probability approaching one as N ! 1, if the asynchronism level grows as O(e ), with below the synchronization threshold, a constant that admits a simple expression depending on the channel. If exceeds the synchronization threshold, any decoder, sequential or nonsequential, locates the sync pattern with an error that tends to one as N ! 1. Hence, a sequential decoder can locate a sync pattern as well as the (nonsequential) maximum-likelihood decoder that operates on the basis of output sequences of maximum length A + N 01, but with far fewer observations.
Originally, the model appears in REF with the goal being to locate a sync pattern at the output of a memoryless channel using a sequential detector without communicating a message to the receiver.
Optimal Sequential Frame Synchronization
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Mathematics Computer Science