Information Theory and Prefix Coding Fundamentals

Information theory provides the mathematical bedrock for data compression, modern communication systems, and machine learning. This course breaks down essential information-theoretic concepts into approachable, step-by-step written explanations and practical exercises. You will start from the foundational definitions of probability distributions and information measures, progressing through optimal binary coding techniques, entropy bounds, and divergence metrics used across modern computing. What you'll learn: - Understand the core principles of binary prefix coding and uniquely decodable codes - Calculate Shannon entropy and determine the theoretical lower bounds on average code length - Analyze Kraft's inequality and its role in prefix code construction - Measure relative entropy and Kullback-Leibler divergence between probability distributions - Evaluate statistical distance (total variation distance) and apply Pinsker's inequality - Explore modern connections between information measures, data compression, and machine learning The course begins with fundamental terminology and probability essentials before moving into detailed proofs, code construction techniques, and analytical problem sets. This course is designed for curious beginners, computer science students, and programmers interested in theoretical computer science. No advanced background in information theory is required. Start reading today to build a rigorous conceptual foundation in information theory.