While coding theory has evolved into an essential ingredient of contemporary information technology, it remains a fascinating area of research where many fundamental ideas of information theory and mathematics meet. Indeed, the diversity and profundity of recent new ideas in, and new applications of, coding theory is impressive.
The following themes were of primary interest at the seminar:. Codes on graphs include turbo codes, low-density parity check codes, and a variety of similar codes.
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Such codes are a perfect nurturing ground for cross-fertilization of ideas between computer science, electrical engineering, and mathematics. The mathematical tools in this area include ideas from graph theory, probability, algebra, discrete mathematics, and statistical physics.
Algebraic coding theory continues to be of supreme theoretical and practical interest. Prime examples of this area are Reed-Solomon codes, codes from algebraic geometry, and codes obtained from algebraically constructed graphs. Recent advances in the field include, in particular, list-decoding algorithms for various classes of algebraic codes. Emerging relationships between this area and codes on graphs appear to be promising for future research.
Polar codes discovered by Arikan in are a breakthrough of utmost significance. Such codes are provably capacity-achieving on very many channels with very low-complexity and very practical encoders and decoders. These codes rely on a new large-system limit that combines information theory and coding theory more smoothly than any prior coding technique. MR hb. Progress in cryptology-Mycrypt First international conference on cryptology in Malaysia, Kuala Lumpur, Malaysia, September , , proceedings. Pierre Loidreau and Raphael Overbeck. Designs Codes and Cryptography.
Springer, Netherlands. Silva and F. IEEE Int. Theory, pp IT] 27 Apr Rashwan, Ernst M. Gabidulin, B.
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IT] 2 Jun WCC Bergen, Norway. Alexander Wachter-Zeh. Thesis, University of Rennes 1. Eraj Khan, Ernst M.
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