Upper Bounds on the Probability of Error in terms of Mean Divergence Measures

TL;DR

This paper derives sharper upper bounds on the probability of error using inequalities involving differences of mean functions, which are convex, providing improved estimates over existing methods.

Contribution

It introduces new bounds on error probability based on mean differences and convexity, enhancing previous inequality-based approaches.

Findings

Established sharper upper bounds on probability of error.

Demonstrated convexity of mean difference functions.

Compared results showing improved bounds over existing inequalities.

Abstract

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of mean considered is convex functions. Applying some properties, upper bounds on the probability of error are established in this paper. It is also shown that the results obtained are sharper than obtained directly applying known inequalities.