Communication under Strong Asynchronism

TL;DR

This paper analyzes asynchronous communication over point-to-point channels, establishing the limits of message detection speed under strong asynchronism and characterizing achievable rates in such regimes.

Contribution

It introduces a precise threshold for reliable communication under exponential asynchronism and characterizes achievable rates with respect to expected delay.

Findings

Vanishing error probability is achievable if asynchronism level grows exponentially with codeword length, up to a threshold.

The synchronization threshold is explicitly characterized and is at least the channel capacity.

A necessary condition for reliable Gaussian channel communication under strong asynchronism is derived.

Abstract

We consider asynchronous communication over point-to-point discrete memoryless channels. The transmitter starts sending one block codeword at an instant that is uniformly distributed within a certain time period, which represents the level of asynchronism. The receiver, by means of a sequential decoder, must isolate the message without knowing when the codeword transmission starts but being cognizant of the asynchronism level A. We are interested in how quickly can the receiver isolate the sent message, particularly in the regime where A is exponentially larger than the codeword length N, which we refer to as `strong asynchronism.' This model of sparse communication may represent the situation of a sensor that remains idle most of the time and, only occasionally, transmits information to a remote base station which needs to quickly take action. The first result shows that vanishing error probability can be guaranteed as N tends to infinity while A grows as Exp(N*k) if and only if k does not exceed the `synchronization threshold,' a constant that admits a simple closed form expression, and is at least as large as the capacity of the synchronized channel. The second result is the characterization of a set of achievable strictly positive rates in the regime where A is exponential in N, and where the rate is defined with respect to the expected delay between the time information starts being emitted until the time the receiver makes a decision. As an application of the first result we consider antipodal signaling over a Gaussian channel and derive a simple necessary condition between A, N, and SNR for achieving reliable communication.