Venkatesan Guruswami and Atri Rudra

Error Correction Up to the Information-Theoretic Limit

Abstract : Ever since the birth of coding theory almost 60 years ago, researchers have been pursuing the elusive goal of constructing the "best codes," whose encoding introduces the minimum possible redundancy for the level of noise they can correct. In this article, we survey recent progress in list decoding that has led to efficient error-correction schemes with an optimal amount of redundancy, even against worst-case errors caused by a potentially malicious channel. To correct a proportion p (say 20%) of worst-case errors, these codes only need close to a proportion p of redundant symbols. The redundancy cannot possibly be any lower information theoretically. This new method holds the promise of correcting a factor of two more errors compared to the conventional algorithms currently in use in diverse everyday applications.
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