標題: Simultaneous Partial Inverses and Decoding Interleaved Reed-Solomon Codes 作者: Yu, Jiun-HungLoeliger, Hans-Andrea電機工程學系Department of Electrical and Computer Engineering 關鍵字: Interleaved Reed-Solomon codes;subfield-evaluation codes;simultanenous partial-inverse problem;Euclidean algorithm;multi-sequence Berlekamp-Massey algorithm;performance bounds 公開日期: 1-Dec-2018 摘要: This paper introduces the simultaneous partial-inverse problem (SPI) for polynomials and develops its application to decoding interleaved Reed-Solomon codes beyond half the minimum distance. While closely related both to standard key equations and to well-known Pade approximation problems, the SPI problem stands out in several respects. First, the SPI problem has a unique solution (up to a scale factor), which satisfies a natural degree bound. Second, the SPI problem can be transformed (monomialized) into an equivalent SPI problem where all moduli are monomials. Third, the SPI problem can be solved by an efficient algorithm of the Berlekamp-Massey type. Fourth, decoding interleaved Reed-Solomon codes (or subfield-evaluation codes) beyond half the minimum distance can be analyzed in terms of a partial-inverse condition for the error pattern: if that condition is satisfied, then the (true) error locator polynomial is the unique solution of a standard key equation and can be computed in many different ways, including the well-known multi-sequence Berlekamp-Massey algorithm and the SPI algorithm of this paper. Two of the best performance bounds from the literature (the Schmidt-Sidorenko-Bossert bound and the Roth-Vontobel bound) are generalized to hold for the partial-inverse condition and thus to apply to several different decoding algorithms. URI: http://dx.doi.org/10.1109/TIT.2018.2868701http://hdl.handle.net/11536/148507 ISSN: 0018-9448 DOI: 10.1109/TIT.2018.2868701 期刊: IEEE TRANSACTIONS ON INFORMATION THEORY Volume: 64 起始頁: 7511 結束頁: 7528 Appears in Collections: Articles