A visual introduction to information theory

TL;DR

This paper offers a visual, intuition-based introduction to core concepts of information theory, explaining how entropy, mutual information, and channel capacity define data compression and reliable communication limits.

Contribution

It provides an accessible, visual explanation of information theory fundamentals, making complex ideas understandable with minimal prior knowledge.

Findings

Clarifies how entropy relates to data compression

Shows how mutual information measures shared information

Explains channel capacity as the maximum reliable transmission rate

Abstract

Information theory, though originally developed for communications engineering, provides mathematical tools with broad applications across science. These tools characterize the fundamental limits of data compression and transmission in the presence of noise. Here, we present a visual, intuition-driven guide to key concepts in information theory. We show how entropy, mutual information, and channel capacity follow from basic probability, and how they determine the shortest possible encoding of a data source and the maximum rate of reliable communication through a noisy channel. Our presentation assumes only a familiarity with basic probability theory.