Log-Quadratic Bounds for the Gaussian Q-function

TL;DR

This paper introduces quadratic bounds for the logarithm of the Gaussian Q-function and provides an analytical method for accurate log-quadratic approximations with minimal error.

Contribution

It proposes a novel quadratic bounding technique and an analytical approach for precise log-quadratic approximations of the Gaussian Q-function.

Findings

Derived bounds with explicit quadratic form for the log of the Q-function

Developed an analytical method for log-quadratic approximation

Achieved approximation accuracy with less than 10^{-3} error

Abstract

We present bounds of quadratic form for the logarithm of the Gaussian Q-function. We also show an analytical method for deriving log-quadratic approximations of the Q-function and give an approximation with absolute error less than $10^{-3}$.