Fast skew-feedback shift-register synthesis

Vladimir Sidorenko; Martin Bossert

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Fast skew-feedback shift-register synthesis

机译：快速的歪斜反馈移位寄存器综合

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摘要

A skew-feedback shift-register is a generalization of a linear-feedback shift-register and can be applied in decoding (interleaved) Reed-Solomon codes or Gabidulin codes beyond half their code distance. A fast algorithm is proposed which synthesizes all shortest skew-feedback shift-registers generating L sequences of varying length over a field. For fixed L, the time complexity of the algorithm is O(M(N) log N) operations, where N is the length of a longest sequence and M(N) is the complexity of the multiplication of two skew polynomials of maximum degree N.

机译：歪斜反馈移位寄存器是线性反馈移位寄存器的概括，可以应用于解码（交织）的Reed-Solomon码或Gabidulin码超过其码距的一半。提出了一种快速算法，该算法可以合成所有最短的歪斜反馈移位寄存器，从而在一个场上生成长度可变的L个序列。对于固定的L，算法的时间复杂度是O（M（N）log N）个运算，其中N是最长序列的长度，而M（N）是两个最大度数N的偏斜多项式相乘的复杂度。

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来源
《Designs, Codes and Crytography》 |2014年第2期|55-67|共13页
作者
Vladimir Sidorenko; Martin Bossert;
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作者单位

Institute of Communications Engineering, Ulm University, Ulm, Germany;

Institute of Communications Engineering, Ulm University, Ulm, Germany;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Shift-register synthesis; Multiple sequences; Skew-feedback; Decoding; Reed-Solomon codes; Gabidulin codes; Interleaved codes;

机译：移位寄存器合成;多个序列;歪斜反馈解码;里德-所罗门码;Gabidulin代码;交错码;

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专利

1. Skew-Feedback Shift-Register Synthesis and Decoding Interleaved Gabidulin Codes [J] . Sidorenko V., Jiang L., Bossert M. Information Theory, IEEE Transactions on . 2011,第2期

机译：斜反馈移位寄存器合成和交错的Gabidulin码解码
2. FAST MULTI-SEQUENCE SHIFT-REGISTER SYNTHESIS WITH THE EUCLIDEAN ALGORITHM [J] . Alexander Zeh, Antonia Wachter Advances in mathematics of communications . 2011,第4期

机译：使用EUCLIDEAN算法快速进行多序列移位寄存器合成
3. Constrained shift-register synthesis: fast GMD decoding of 1D algebraic codes [J] . Yutaka Kobayashi, Masaya Fujisawa, Shojiro Sakata Electronics and communications in Japan. Part 3 . 2000,第4期

机译：受限移位寄存器综合：一维代数代码的快速GMD解码
4. Generalised Multi-sequence Shift-Register synthesis using module minimisation [C] . Nielsen Johan S.R. IEEE International Symposium on Information Theory . 2013

机译：使用模块最小化的通用多序列移位寄存器综合
5. Architectural optimizations and synthesis tools for improved energy efficiency and faster design closure for FPGAs. [D] . Mondal, Somsubhra. 2007

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7. Fast Multi-Sequence Shift-Register Synthesis with the Euclidean Algorithm [O] . Zeh Alexander, Wachter Antonia 2011

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8. Implementation of the Berlekamp-Massey Linear Feedback Shift-Register Synthesis211 Algorithm in the C Programming Language [R] . Campbell, P. L. 1999

机译：用C编程语言实现Berlekamp-massey线性反馈移位寄存器synthesis211算法

Fast skew-feedback shift-register synthesis

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