An Introduction to Galois Fields and Reed-Solomon Codes

Abstract:
'Galois fields' are sets of finitely many elements on which one can define the most basic of arithmetic operations: addition, subtraction, multiplication and division. Finite fields, also known as Galois fields, have a rich theory and play a key role in several areas of Computer Science, Mathematics and Electrical Engineering, such as in cryptography, number theory and error correction coding. This talk will provide a naive and elementary introduction to the theory of finite fields. We will begin with the set of integers and use the long division technique and the remainder operation to construct fields of all possible finite sizes. As an application to coding theory, the talk will then introduce Reed-Solomon codes from the perspective of correcting erasures in communication or data storage. 

The talk will not assume any prior mathematical knowledge or engineering background.

About the speaker:
Lakshmi Prasad Natarajan is an Assistant Professor in the Department of Electrical Engineering, Indian Institute of Technology Hyderabad. He received the Ph.D. degree from the Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, in 2013. Between 2014 and 2016 he held a post-doctoral position at the Department of Electrical and Computer Systems Engineering, Monash University, Australia. His primary research interests are coding techniques and information theory for communication systems.
Dr. Natarajan is an Editor of the IEEE Wireless Communications Letters. He was the recipient of the Seshagiri-Kaikini Medal 2013-14 for best Ph.D. thesis, Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore. He served in the organizing committee of the 2018 National Conference on Communications, Hyderabad, the 2016 Australian Communications Theory Workshop, Melbourne and the 2016 Australian Information Theory School, Melbourne.