An improved estimate of the inverse binary entropy function

TL;DR

This paper introduces two new estimates for the inverse binary entropy function, with one providing a close approximation especially at higher entropy values, leveraging information theory and population genetics insights.

Contribution

It presents novel estimates for the inverse binary entropy function, improving approximation accuracy over existing methods.

Findings

Second estimate closely matches the actual inverse binary entropy values.

Approximation accuracy improves away from low entropy regions.

Utilizes concepts from information theory and population genetics.

Abstract

Two estimates for the inverse binary entropy function are derived using the property of information entropy to estimate combinatorics of sequences as well as related formulas from population genetics for the effective number of alleles. The second estimate shows close correspondence to the actual value of the inverse binary entropy function and can be seen as a close approximation away from low values of binary entropy where $p$ or $1-p$ are small.