An information diffusion Fano inequality

TL;DR

This paper introduces a new, general Fano-type inequality derived from an elementary argument, unifying and extending existing Fano inequalities for information diffusion analysis.

Contribution

It presents a novel, unified Fano inequality that generalizes previous versions, providing a broader tool for information diffusion analysis.

Findings

Unifies various Fano inequalities into a single general form

Provides an elementary derivation of the diffusion inequality

Extends the applicability of Fano inequalities in information theory

Abstract

In this note, we present an information diffusion inequality derived from an elementary argument, which gives rise to a very general Fano-type inequality. The latter unifies and generalizes the distance-based Fano inequality and the continuous Fano inequality established in [Corollary 1, Propositions 1 and 2, arXiv:1311.2669v2], as well as the generalized Fano inequality in [Equation following (10); T. S. Han and S. Verd\'u. Generalizing the Fano inequality. IEEE Transactions on Information Theory, 40(4):1247-1251, July 1994].