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Algorithmic Results in List Decoding (Foundations and Trends

Algorithmic Results in List Decoding introduces and motivates the problem of list decoding, and discusses the central algorithmic results of the subject, culminating with the recent results on achieving "list decoding capacity." The main technical focus is on giving a complete presentation of the recent algebraic results achieving list decoding capacity, while pointers or brief descriptions are provided for other works on list decoding. Algorithmic Results in List Decoding is intended for scholars and graduate students in the fields of theoretical computer science and information theory. The author concludes by posing some interesting open questions and suggests directions for future work.
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Table of Contents

1. Introduction; 2. Definitions and Terminology; 3. Combinatorics of List Decoding; 4. Decoding Reed-Solomon Codes; 5. Graph-based List-Decodable Codes; 6. Folded Reed-Solomon Codes; 7. Achieving Capacity over Bounded Alphabets; 8. Concluding Thoughts; References

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