| The generalized Goertzel algorithm and its parallel hardware implementation |
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| 基金项目： | This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 60433050, 90607005) |
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| 摘 要： | Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) error correcting codes are widely used in digital technology. An important problem in the implementation of RS and BCH decoding is the fast finding of the error positions (the roots of error locator polynomials). Several fast root-finding algorithms for polynomials over finite fields have been proposed. In this paper we give a generalization of the Goertzel algorithm. Our algorithm is suitable for the parallel hardware implementation and the time of multiplications used is restricted by a constant.
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| 收稿时间： | 17 May 2006 |
| 修稿时间： | 14 August 2007 |
The generalized Goertzel algorithm and its parallel hardware implementation |
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| Authors: | Chen Hao Chen GongLiang and Li JianHua |
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| Institution: | (1) Software Engineering Institute, East China Normal University, Shanghai, 200062, China;(2) School of Information Security Engineering, Department of Electronic Engineering, Shanghai JiaoTong University, Shanghai, 200030, China |
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| Abstract: | Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) error correcting codes are widely used in digital technology. An important problem in the implementation of RS and BCH decoding is the fast finding of the error positions (the roots of error locator polynomials). Several fast root-finding algorithms for polynomials over finite fields have been proposed. In this paper we give a generalization of the Goertzel algorithm. Our algorithm is suitable for the parallel hardware implementation and the time of multiplications used is restricted by a constant. |
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| Keywords: | number theory of finite field RS and BCH decoding normal base the Goertzel algorithm |
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