Topic:

Advanced Algebraic Methodology With Applications to Error-Correcting Codes
 

Speaker:

李崇道 教授 Prof. Chong-Dao Lee

 

義守大學通訊工程學系
Dept. of Communication Engineering,
I-Shou University

 

Language :

Chinese

 

Date:

2020/05/15

 

Time:

14:20~

 

Location: 

Delta building R216, NTHU

 

Abstract:

Cyclic codes, which include the well-known Bose-Chaudhuri-Hocquenghem (BCH), Reed-
Solomon (RS), and quadratic residue codes, are a large and important class of error-
correcting codes over Galois fields. Owing to different algebraic descriptions of cyclic codes in
matrix and polynomial forms, their decoding procedures have been extensively studied over a
half century. First of all, it has also been shown that the majority logic decoding proposed by
Reed is one of the simplest algorithms for decoding cyclic codes. Peterson described an
algebraic decoding algorithm for binary BCH codes. Generally speaking, the algebraic
decoding algorithm consists of three steps: 1) Calculate the syndromes from a received word.
2) Determine the error positions. 3) Evaluate the error values. In the algorithm, the error
locators as well as syndrome matrices are adopted. Subsequently, a fast shift-register-based
algorithm, which is now known as the Berlekamp-Massey algorithm, is a very efficient method
for decoding BCH and RS codes. Codes of these two classes have been widely used in data
storage systems and wireless communication systems.
In this talk, the concept of weak locators, radical locators, and partial syndrome matrices
are introduced. They are very helpful to develop various algebraic methods such that the
decoding of cyclic codes brings about significant computational benefits and memory cost
reduction.

 

Short Bio:

 

 義守大學應用數學系學士、資訊工程系碩博士畢業。榮獲IEEE Senior Member (2016-present)。獲得7項國內外專利（其中美國專利1件、大陸專利1件，其餘為臺灣專利）並發表SCI學術期刊論文32篇（其中IEEE期刊23篇，9篇在旗艦期刊Transactions on Information Theory、5篇在Transactions on Communications、7篇在Communications Letters、2篇在Signal Processing Letters）。獲得科技部電信學門個人專題計畫(2008-2020)，補助總金額超過1千萬元。擔任IEEE Information Theory Society Tainan Chapter副主席(2017-2018)。兼任義守大學圖書與資訊處副處長(2018-present)。廈門大學短期研究(2014)、上海師範大學、華東師範大學、四川師範大學、西南交通大學專題演講(2019)、兼任教師 樹德科技大學電腦與通訊工程學系、高雄大學應用數學系。