Optimal Sequential Frame Synchronization

TL;DR

This paper establishes the fundamental limits of sequential frame synchronization, showing that optimal detection is possible under certain growth conditions of asynchronism, matching limits known for reliable asynchronous communication.

Contribution

It characterizes the exact conditions under which sequential decoders can reliably locate sync patterns, matching the synchronization threshold for asynchronous communication.

Findings

Sequential decoder can exactly locate sync pattern without delay below the threshold.

Synchronization threshold depends on the channel and determines the feasibility of reliable detection.

Sequential decoding achieves similar performance to maximum likelihood decoding with fewer observations.

Abstract

We consider the `one-shot frame synchronization problem' where a decoder wants to locate a sync pattern at the output of a channel on the basis of sequential observations. We assume that the sync pattern of length N starts being emitted at a random time within some interval of size A, that characterizes the asynchronism level between the transmitter and the receiver. We show that a sequential decoder can optimally locate the sync pattern, i.e., exactly, without delay, and with probability approaching one as N tends to infinity, if and only if the asynchronism level grows as O(exp(N*k)), with k below the `synchronization threshold,' a constant that admits a simple expression depending on the channel. This constant is the same as the one that characterizes the limit for reliable asynchronous communication, as was recently reported by the authors. If k exceeds the synchronization threshold, any decoder, sequential or non-sequential, locates the sync pattern with an error that tends to one as N tends to infinity. Hence, a sequential decoder can locate a sync pattern as well as the (non-sequential) maximum likelihood decoder that operates on the basis of output sequences of maximum length A+N-1, but with much fewer observations.