The AWGN Red Alert Problem

TL;DR

This paper characterizes the optimal error exponent for the 'red alert' message in AWGN channels, ensuring extremely low missed detection probability while maintaining overall error and false alarm rates.

Contribution

It provides a complete characterization of the red alert exponent specifically for AWGN channels with power constraints, extending previous discrete channel results.

Findings

Optimal red alert exponent derived for AWGN channels

Achieves low missed detection probability under power constraints

Extends previous discrete channel results to continuous channels

Abstract

Consider the following unequal error protection scenario. One special message, dubbed the "red alert" message, is required to have an extremely small probability of missed detection. The remainder of the messages must keep their average probability of error and probability of false alarm below a certain threshold. The goal then is to design a codebook that maximizes the error exponent of the red alert message while ensuring that the average probability of error and probability of false alarm go to zero as the blocklength goes to infinity. This red alert exponent has previously been characterized for discrete memoryless channels. This paper completely characterizes the optimal red alert exponent for additive white Gaussian noise channels with block power constraints.