应我校电信学院于启月教授邀请，信息论与编码、信息安全领域的国际著名学者韩永祥教授（IEEE Fellow），将来我校访问讲学和交流研讨。

韩永祥教授将分别于2024年9月18日、9月19日和9月20日在科创大厦黄大年茶思屋进行三场学术讲座，讲座将重点讨论Reed-Solomon码的最新研究进展及有限域上的快速傅里叶变换算法等前沿课题。欢迎全校感兴趣的师生参加。

讲学时间：2024年9月18日上午 9:00-12:00

讲学地点：科创大厦黄大年茶思屋

讲学题目: From Finite Fields to Reed-Solomon Code

报告内容简介：

This lecture will offer an accessible yet comprehensive introduction to the theory of Reed-Solomon codes, a technology widely used in various communication systems such as deep space communication, storage, and broadcasting. First, the lecture will introduce the relevant theory of finite fields, covering topics such as prime fields, extension fields, polynomials over fields, the extended Euclidean algorithm, and other foundational concepts. This will lead to the definition of linear block codes, including their structure and the Singleton Bound. Building on the Singleton Bound, the definition of Reed-Solomon codes will be introduced, along with the classical encoding algorithms for Reed-Solomon codes. Professor Han will then provide a detailed explanation of the classical decoding algorithms for Reed-Solomon codes. This lecture will serve as the foundation for the subsequent two lectures.

讲学时间：2024年9月19日下午 14:00-17:00

讲学地点：科创大厦黄大年茶思屋

讲学题目：Applications of RS Codes and an Introduction to Fourier Transform over Finite Fields

报告内容简介：

The first part of this lecture will build upon the foundational theory of Reed-Solomon codes discussed in the previous lecture and further explore how Reed-Solomon codes can be applied in secure wireless sensor networks. This work, published in the paper “A Pairwise Key Pre-distribution Scheme for Wireless Sensor Networks”, has been cited over 2,500 times and received the 2013 ACM CCS Test-of-Time Award.  The second part will introduce the fundamentals of Fourier transforms over finite fields and present the Fast Fourier Transform (FFT) algorithm in this context, which breaks decades of stagnation in the field by reducing the computational complexity to O(nlg(n)).

讲学时间：2024年9月20日上午 9:00-12:00

讲学地点：科创大厦黄大年茶思屋

讲学题目:  Fast Fourier Transform for Finite Fields and Its Applications to Reed-Solomon Codes

报告内容简介：

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(nlg(n)), where n is the number of points evaluated in FFT. In this paper, we reformulate this FFT algorithm, such that it can be easier understood and be extended to develop frequency domain decoding algorithms for (n = 2^m , k) systematic Reed-Solomon (RS) codes over F₂^m , m ∈ Z⁺ , 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(nlg(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-Tukey FFTs. As revealed by the computer simulations, the proposed decoding algorithm is 50 times faster than the conventional one for the (2¹⁶ , 2¹⁵ ) RS code over F₂₁₆

报告人简介：