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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 Forney algorithm ： ウィキペディア英語版 Forney algorithm In coding theory, the Forney algorithm (or Forney's algorithm) calculates the error values at known error locations. It is used as one of the steps in decoding BCH codes and Reed–Solomon codes (a subclass of BCH codes). George David Forney, Jr. developed the algorithm. ==Procedure== :''Need to introduce terminology and the setup...'' Code words look like polynomials. By design, the generator polynomial has consecutive roots αc, α''c''+1, ..., α''c''+''d''−2. Syndromes Error location polynomial :$\backslash Lambda(x)\; =\; \backslash prod\_^\backslash nu\; (1-\; x\; \backslash ,\; X\_i)\; =\; 1\; +\; \backslash sum\_^\backslash nu\; \backslash lambda\_i\; \backslash ,\; x^i$ The zeros of Λ(''x'') are ''X''1−1, ..., ''X''''ν''−1. The zeros are the reciprocals of the error locations $X\_j\; =\; \backslash alpha^$. Once the error locations are known, the next step is to determine the error values at those locations. The error values are then used to correct the received values at those locations to recover the original codeword. In the more general case, the error weights can be determined by solving the linear system :$s\_0\; =\; e\_1\; \backslash alpha^\; +\; e\_2\; \backslash alpha^\; +\; \backslash cdots\; \backslash ,$ :$s\_1\; =\; e\_1\; \backslash alpha^\; +\; e\_2\; \backslash alpha^\; +\; \backslash cdots\; \backslash ,$ :$\backslash cdots\; \backslash ,$ However, there is a more efficient method known as the Forney algorithm, which is based on Lagrange interpolation. First calculate the error evaluator polynomial :$\backslash Omega(x)\; =\; S(x)\backslash ,\backslash Lambda(x)\; \backslash pmod\; x^.$ Then evaluate the error values:〔 :$e\_j\; =\; -\; \backslash frac)\}\; \backslash ,$ The value is often called the "first consecutive root" or "fcr". Some codes select , so the expression simplifies to: :$e\_j\; =\; -\; \backslash frac$ 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「Forney algorithm」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.