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The focus of this course is on modern coding theory. In contrast to classical coding theory, which finds its roots in algebra, modern coding theory refers to a broad family of coding techniques unified by the use of sparse-graph constructions, iterative decoding algorithms, and probabilistic methods. For this reason, modern codes are also sometimes referred to as graph-based codes or probabilistic codes. Iterative message-passing methods have revolutionized coding, and more generally, communications and storage. The course covers recent advances in modern coding theory: (capacity-achieving) spatially-coupled codes, turbo-like codes, product-like codes from a modern coding theory lens, coding for ultra high-throughput applications, neural decoders, and the application of coding to areas beyond communication and storage. The course will cover the following content: 1. Factor graphs 2. LDPC codes (review) 3. Spatially-coupled LDPC codes 4. Turbo-like codes 5. Spatially-coupled turbo-like codes 6. Product-like codes from a modern coding theory lens 7. LDPC decoders for high-throughput applications 8. Product-like decoders for high-throughput applications 9. Rateless codes 10. Neural decoders for linear block codes 11. Applications of (graph-based) coding beyond communications and storage

Basic channel coding