Fundamentals of Error-Correcting Codes and Coding Theory

Reliable digital communication and data storage depend on the ability to detect and repair data corruption. This text-based course introduces the core principles of coding theory and error-correcting codes, breaking down complex mathematical concepts into clear, digestible explanations and practical examples. You will build a solid understanding of how modern systems protect information across noisy channels, starting with foundational definitions and progressing to classical block codes. What you'll learn: - Understand core concepts of information transmission, code distance, and error detection versus correction - Analyze linear block codes using generator and parity-check matrices - Explore theoretical limits including the Hamming, Gilbert-Varshamov, and Singleton bounds - Construct and decode standard Hamming codes for single-error correction - Master the principles and algebraic structure of Reed-Solomon codes - Examine concatenated coding architectures and modern applications in distributed storage and network protocols The course begins with fundamental terminology and linear algebra prerequisites before guiding you step-by-step through specific coding constructions, theoretical bounds, and decoding algorithms with written walkthroughs. Designed for curious learners, computer science students, and software engineers with a basic background in high school algebra; no prior knowledge of coding theory is required. Start reading today to master the mathematical foundations that keep modern digital data intact.