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The fourth volume of Rudolf Ahlswede’s lectures on Information Theory emphasizes Combinatorics, driven by his interest in zero-error codes, which shift coding problems from probabilistic to combinatorial frameworks. A key example is Shannon’s zero-error capacity, which involves analyzing independent sets in graphs, and extends to the Zarankiewicz problem in multiple access channels. Codes are viewed combinatorially as hypergraphs, allowing for the application of various colouring and covering techniques to derive coding theorems. The book also explores codes generated by permutations and delves into extremal problems in Combinatorics. The first part focuses on combinatorial methods for analyzing classical codes, such as prefix codes and those in the Hamming metric, while the second part addresses combinatorial models in Information Theory, where codes are based on combinatorial structures in multiple access channels and refined distortions. Orthogonal polynomials serve as analytical tools, particularly in the study of perfect codes. Covering classical information processing tasks—knowledge acquisition, data storage, transmission, and concealment—the lectures are designed for graduate students in Mathematics and those in Theoretical Computer Science, Physics, and Electrical Engineering. They can serve as course foundations or supplements, while Ph.D. students may find research problems and conjectures for thesis topics, and adv
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Combinatorial Methods and Models, Rudolf Ahlswede
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- 2018
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