A Chernoff-type Lower Bound for the Gaussian Q-function

TL;DR

This paper introduces a new Chernoff-type lower bound for the Gaussian Q-function, providing a simple exponential form with parameters, proven through inequalities involving related functions.

Contribution

It presents a novel lower bound for the Gaussian Q-function using a parametric exponential form and a proof based on inequalities between related functions.

Findings

The lower bound is expressed as a single exponential function.

The bound is proven using inequalities involving related functions.

The approach provides a potentially tighter or more convenient bound.

Abstract

A lower bound for the Gaussian Q-function is presented in the form of a single exponential function with parametric order and weight. We prove the lower bound by introducing two functions, one related to the Q-function and the other similarly related to the exponential function, and by obtaining inequalities that indicate the sign of the difference of the two functions.