文章基本信息

标题：Two Theorems in List Decoding
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作者：atri rudra, steve uurtamo
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2010
卷号：2010
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We prove the following results concerning the list decoding of error-correcting codes: We show that for any code with a relative distance of (over a large enough alphabet), the following result holds for random errors: With high probability, for a −\eps fraction of random errors (for any \eps0), the received word will have only the transmitted codeword in a Hamming ball of radius around it. Thus, for random errors, one can correct twice the number of errors uniquely correctable from worst-case errors for any code. A variant of our result also gives a simple algorithm to decode Reed-Solomon codes from random errors that, to the best of our knowledge, runs faster than known algorithms for certain ranges of parameters. We show that concatenated codes can achieve the list decoding capacity for erasures. A similar result for worst-case errors was proven by Guruswami and Rudra (SODA 08), although their result does not directly imply our result. Our results show that a subset of the random ensemble of codes considered by Guruswami and Rudra also achieve the list decoding capacity for erasures.
关键词：Error-correcting codes, List decoding