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| HAL: hal-00645738, version 1 |
| DOI: 10.1109/TIT.2011.2162160 |
| See detailed view |  BibTeX,EndNote,... |
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| IEEE Transactions on Information Theory 57 (2011) 5946-5959 |
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| An Interpolation Procedure for List Decoding Reed-Solomon Codes Based on Generalized Key Equations |
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| Alexander Zeh 1, 2Christian Gentner 3 |
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| (2011-09) |
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| The key step of syndrome-based decoding of Reed-Solomon codes up to half the minimum distance is to solve the so-called Key Equation. List decoding algorithms, capable of decoding beyond half the minimum distance, are based on interpolation and factorization of multivariate polynomials. This article provides a link between syndrome-based decoding approaches based on Key Equations and the interpolation-based list decoding algorithms of Guruswami and Sudan for Reed-Solomon codes. The original interpolation conditions of Guruswami and Sudan for Reed-Solomon codes are reformulated in terms of a set of Key Equations. These equations provide a structured homogeneous linear system of equations of Block-Hankel form, that can be solved by an adaption of the Fundamental Iterative Algorithm. |
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| 1: | TANC (INRIA Saclay - Ile de France) |
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INRIA – Polytechnique - X – CNRS : UMR7161 |
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| 2: | Institute of Communications Engineering [Ulm] (INT - University of Ulm.) |
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University of Ulm |
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| 3: | German Aerospace Center (DLR) |
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Deutsches Zentrum für Luft- und Raumfahrt (DLR) |
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| 4: | Laboratoire d'informatique de l'école polytechnique (LIX) |
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CNRS : UMR7161 – Polytechnique - X |
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| Domain | : | Computer Science/Information Theory and Coding Mathematics/Information Theory |
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| Attached file list to this document: | |||||
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| hal-00645738, version 1 | |
| http://hal.inria.fr/hal-00645738 | |
| oai:hal.inria.fr:hal-00645738 | |
| From: Alexander Zeh | |
| Submitted on: Monday, 28 November 2011 15:40:46 | |
| Updated on: Monday, 16 July 2012 08:57:04 | |
