A General Characterization of Sync Word for Asynchronous Communication

TL;DR

This paper characterizes the fundamental limits of frame synchronization in asynchronous communication, revealing a tradeoff between sync frame length and channel parameters like power, extending previous results from discrete memoryless channels to AWGN channels.

Contribution

It introduces a unified framework for understanding sync word requirements across different channel types, including a novel analysis of energy scaling for AWGN channels.

Findings

Synchronization threshold $eta(Q)$ for DMCs is characterized.

Tradeoff between sync frame length and input power in AWGN channels is established.

Scaling laws for energy-efficient synchronization are derived.

Abstract

We study a problem of sequential frame synchronization for a frame transmitted uniformly in $A$ slots. For a discrete memoryless channel (DMC), Venkat Chandar et al showed that the frame length $N$ must scale with $A$ as $e^{N \alpha(Q)} > A$ for the frame synchronization error to go to zero (asymptotically with $A$). Here, $Q$ denotes the transition probabilities of the DMC and $\alpha(Q)$, 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 $E = N P$ for optimal frame synchronisation.