Coding Theory

Hans-Andrea Loeliger, Emina Soljanin, Judy Walker, Hans-Andrea Loeliger, Emina Soljanin, Judy Walker, Hans-Andrea Loeliger, Emina Soljanin, Judy Walker, Dagstuhl Reports
<span class="release-stage">unpublished</span>
Coding theory has become an essential ingredient of contemporary information technology, and it remains a fascinating area of research. The seminar brought together 45 high-caliber researchers with backgrounds and interests in various different parts of coding theory. The new area of codes for cloud applications received much attention, but other key areas such as network codes, codes on graphs, algebraic coding, and polar codes, were also well represented and generated lively discussions.
more &raquo; ... se Creative Commons BY 3.0 Unported license © Hans-Andrea Loeliger, Emina Soljanin, and Judy Walker 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. Due to the recent new idea of "spatial coupling", such codes can now be designed to achieve the Shannon capacity of most communication channels with practical encoders and decoders. 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
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