Topic
List decoding
About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.
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TL;DR: A general algorithm, applicable to a wide range of constrained interpolation problems in coding theory and systems theory, including list decoding and M-Pade approximation is presented.
54 citations
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27 Jun 2004TL;DR: It is shown that the error probability for decoding interleaved Reed-Solomon Codes with the decoder found by Bleichenbacher et al. is upper bounded by O(1/q), independently of n.
Abstract: We show that the error probability for decoding interleaved Reed-Solomon Codes with the decoder found by Bleichenbacher et al. (Ref.1) is upper bounded by O(1/q), independently of n. The decoding algorithm presented here is similar to that of standard RS codes. It involves computing the error-locator polynomial. These polynomials are found by computing the right kernel of the matrix. The correct solution is always in the right kernel, and so we can correctly decode if the right kernel is one-dimensional
54 citations
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24 Jun 2007TL;DR: It is shown that the error correction problem in random network coding is closely related to a generalized decoding problem for rank-metric codes, and an efficient decoding algorithm is proposed that can correct e errors, mu erasures and v deviations.
Abstract: It is shown that the error correction problem in random network coding is closely related to a generalized decoding problem for rank-metric codes. This result enables many of the rich tools devised for the rank metric to be naturally applied to random network coding. The generalized decoding problem introduced in this paper allows partial information about the error to be supplied. This partial information can be either in the form of erasures (knowledge of an error location but not its value) or deviations (knowledge of an error value but not its location). For Gabidulin codes, an efficient decoding algorithm is proposed that can correct e errors, mu erasures and v deviations, provided 2isin + mu + v les d - 1, where d is the minimum distance of the code.
54 citations
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01 Jun 2013
TL;DR: This work considers Reed-Solomon codes whose evaluation points belong to a subfield, and gives a linear-algebraic list decoding algorithm that can correct a fraction of errors approaching the code distance, while pinning down the candidate messages to a well-structured affine space of dimension a constant factor smaller than the code dimension.
Abstract: We consider Reed-Solomon (RS) codes whose evaluation points belong to a subfield, and give a linear-algebraic list decoding algorithm that can correct a fraction of errors approaching the code distance, while pinning down the candidate messages to a well-structured affine space of dimension a constant factor smaller than the code dimension. By pre-coding the message polynomials into a subspace-evasive set, we get a Monte Carlo construction of a subcode of Reed-Solomon codes that can be list decoded from a fraction (1-R-e) of errors in polynomial time (for any fixed e > 0) with a list size of O(1/e). Our methods extend to algebraic-geometric (AG) codes, leading to a similar claim over constant-sized alphabets. This matches parameters of recent results based on folded variants of RS and AG codes. but our construction here gives subcodes of Reed-Solomon and AG codes themselves (albeit with restrictions on the evaluation points).Further, the underlying algebraic idea also extends nicely to Gabidulin's construction of rank-metric codes based on linearized polynomials. This gives the first construction of positive rate rank-metric codes list decodable beyond half the distance, and in fact gives codes of rate R list decodable up to the optimal (1-R-e) fraction of rank errors. A similar claim holds for the closely related subspace codes studied by Koetter and Kschischang.We introduce a new notion called subspace designs as another way to pre-code messages and prune the subspace of candidate solutions. Using these, we also get a deterministic construction of a polynomial time list decodable subcode of RS codes. By using a cascade of several subspace designs, we extend our approach to AG codes, which gives the first deterministic construction of an algebraic code family of rate R with efficient list decoding from 1-R-e fraction of errors over an alphabet of constant size (that depends only on e). The list size bound is almost a constant (governed by log* (block length)), and the code can be constructed in quasi-polynomial time.
54 citations
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06 Jan 2010TL;DR: In this article, a decoding method is proposed for decoding a first decoding method and decoding a second decoding method when decoding of the first decoding algorithm fails, where the decoding method includes updating multiple variable nodes and multiple check nodes using probability values of received data.
Abstract: A decoding method includes performing a first decoding method and performing a second decoding method when decoding of the first decoding method fails. The first decoding method includes updating multiple variable nodes and multiple check nodes using probability values of received data. The second decoding method includes selecting at least one variable node from among the multiple variable nodes; correcting probability values of data received in the selected at least one variable node; updating the variable nodes and the check nodes using the corrected probability values; and determining whether decoding of the second decoding method is successful.
54 citations