Typicality Graphs:Large Deviation Analysis

TL;DR

This paper introduces the concept of typicality graphs for finite alphabet joint distributions, analyzing their properties and providing a formal framework for representing jointly typical sequences.

Contribution

It formally defines typicality graphs and investigates their properties, advancing the theoretical understanding of large deviation analysis in information theory.

Findings

Defined typicality graphs for joint distributions.

Analyzed properties of these graphs.

Provided a formal framework for large deviation analysis.

Abstract

Let $\mathcal{X}$ and $\mathcal{Y}$ be finite alphabets and $P_{XY}$ a joint distribution over them, with $P_X$ and $P_Y$ representing the marginals. For any $\epsilon > 0$, the set of $n$-length sequences $x^n$ and $y^n$ that are jointly typical \cite{ckbook} according to $P_{XY}$ can be represented on a bipartite graph. We present a formal definition of such a graph, known as a \emph{typicality} graph, and study some of its properties.