Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
نویسندگان
چکیده
منابع مشابه
Explicit Capacity-Achieving List-Decodable Codes or Decoding Folded Reed-Solomon Codes up to their Distance
For every 0 < R < 1 and ε > 0, we present an explicit construction of error-correcting codes of rate R that can be list decoded in polynomial time up to a fraction (1 − R − ε) of errors. These codes achieve the “capacity” for decoding from adversarial errors, i.e., achieve the optimal trade-off between rate and error-correction radius. At least theoretically, this meets one of the central chall...
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We construct an explicit family of linear rank-metric codes over any field Fh that enables efficient list decoding up to a fraction ρ of errors in the rank metric with a rate of 1− ρ− ε, for any desired ρ ∈ (0, 1) and ε > 0. Previously, a Monte Carlo construction of such codes was known, but this is in fact the first explicit construction of positive rate rank-metric codes for list decoding bey...
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We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every 0 < R < 1 and ε > 0, we present an explicit construction of error-correcting codes of rate R that can be list decoded in polynomial time up to a fraction (1 − R − ε) of errors. At least theoretically, this meets one of the cen...
متن کاملList decoding of error correcting codes
Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental algorithmic challenge in coding theory and practice is to efficiently decode the original transmitted message even when a few symbols of the received word are in error. The naive search algorithm runs in exponential time, and several classi...
متن کاملAlgebraic list-decoding of error-correcting codes
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2008
ISSN: 0018-9448
DOI: 10.1109/tit.2007.911222