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FFT Algorithm for Binary Extension Finite Fields and its Application to Reed-Solomon Codes
时间:2018-01-22 11:13    点击:   所属单位:通信工程学院
讲座名称 FFT Algorithm for Binary Extension Finite Fields and its Application to Reed-Solomon Codes
讲座时间 2018-01-25 10:30:00
讲座地点 北校区新科技楼1012报告厅
讲座人 林宪正
讲座人介绍

林宪正博士目前任职中国科技大学信息特任研究员。分别于200420082010年于台湾交通大学获得学士,硕士,博士学位。20102014年,在台湾中央研究院担任博士后研究员。2014年至2016年,在沙特国王科技大学(KAUST)担任博士后研究员。于2015年获得中科院百人计划C类入选,并于20163月至中国科学技术大学任职特聘研究员。 

林博士目前主要研究方向为信道编码算法与应用于存储系统的纠删码设计。硕博期间,他的研究方向为信息隐藏与可视密码。在中研院期间,其研究方向为MIMO算法与代数码的快速算法。在KAUST期间,其主要研究方向为代数码与其应用。目前其主要论文发表于IEEE tran. Information Theory, IEEE tran. Information Forensics and Security, IEEE tran. Communications等期刊。

讲座内容 Recently, a new polynomial basis over binary extension fields was proposed such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order O(n lg(n)), where n is the number of points evaluated in FFT. In this work, we reformulate this FFT algorithm such that it can be easier understood and be extended to develop frequency-domain decoding algorithms for (n=2m, k) systematic Reed-Solomon~(RS) codes over $F_{2m}, mÎZ+, with n-k a power of two. First, the basis of syndrome polynomials is reformulated in the decoding procedure so that the new transforms can be applied to the decoding procedure. A fast extended Euclidean algorithm is developed to determine the error locator polynomial. The computational complexity of the proposed decoding algorithm is O(n\lg(n-k)+(n-k) lg2(n-k)), improving upon the best currently available decoding complexity O(n lg2(n) lglg(n)), and reaching the best known complexity bound that was established by Justesen in 1976. However, Justesen's approach is only for the codes over some specific fields, which can apply Cooley-Tucky FFTs. As revealed by the computer simulations, the proposed decoding algorithm is 50 times faster than the conventional one for the (2^16, 2^15) RS code over $F_{2^16}$.
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