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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Folded Reed–Solomon code ： ウィキペディア英語版 Folded Reed–Solomon code In coding theory, folded Reed–Solomon codes are like Reed–Solomon codes, which are obtained by mapping $m$ Reed–Solomon codewords over a larger alphabet by careful bundling of codeword symbols. Folded Reed–Solomon codes are also a special case of Parvaresh–Vardy codes. Using optimal parameters one can decode with a rate of ''R'', and achieve a decoding radius of 1 − ''R''. The term "folded Reed–Solomon codes" was coined in a paper by V.Y. Krachkovsky with an algorithm that presented Reed–Solomon codes with many random "phased burst" errors (). The list-decoding algorithm for folded RS codes corrects beyond the $1-\backslash sqrt$ bound for Reed–Solomon codes achieved by the Guruswami–Sudan algorithm for such phased burst errors. ==History== One of the ongoing challenges in Coding Theory is to have error correcting codes achieve an optimal trade-off between (Coding) Rate and Error-Correction Radius. Though this may not be possible to achieve practically (due to Noisy Channel Coding Theory issues), quasi optimal tradeoffs can be achieved theoretically. Prior to Folded Reed–Solomon codes being devised, the best Error-Correction Radius achieved was $1-\; \backslash sqrt$, by Reed–Solomon codes for all rates $R$. An improvement upon this $1-\; \backslash sqrt$ bound was achieved by Parvaresh and Vardy for rates . For $R\backslash to\; 0$, the Parvaresh–Vardy algorithm can decode a fraction $1-\; O(R\; \backslash log(1/R))$ of errors. Folded Reed–Solomon Codes improve on these previous constructions, and can be list decoded in polynomial time for a fraction $(1-R-\backslash epsilon)$ of errors for any constant $\backslash epsilon\; >\; 0$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Folded Reed–Solomon code」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.