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.

翻译：信息论虽最初为通信工程而发展，但其提供的数学工具在科学领域具有广泛应用。这些工具刻画了噪声环境下数据压缩与传输的基本极限。本文提出一种可视化、直觉驱动的信息论核心概念指南。我们展示了熵、互信息和信道容量如何从基础概率论推导而来，以及它们如何决定数据源的最短可能编码和噪声信道中可靠通信的最大速率。本阐述仅需读者具备基础概率论知识。