The Mathematics of Reliable Communication
A Journey Through Coding Theory and Real Number Foundations
You've encountered the elegant world of coding theory, but the mathematical foundations—especially those rooted in real numbers—remain frustratingly abstract. The gap between theoretical concepts and practical understanding can feel insurmountable, leaving you uncertain about how these ideas connect to real-world applications. This book bridges that divide by presenting coding theory through the lens of real number mathematics, making complex concepts accessible without sacrificing rigor. You'll discover how error-correcting codes work at a fundamental level, explore the mathematical structures that make reliable communication possible, and understand the deep connections between algebra, analysis, and information theory. From the basics of vector spaces over real fields to advanced topics like lattice codes and sphere packing, each concept builds naturally on the last. You'll gain insight into why certain codes perform better than others, how to analyze their properties mathematically, and what makes coding theory both beautiful and practical. Whether you're strengthening your theoretical foundation or seeking to apply these principles in your work, this book provides the clarity and depth you need to master coding theory's mathematical essence.
Est. Length
253 pages (12 chapters)
Language
English
Publication date
Oct 31, 2025
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