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.
