ECE 7670
Lecture 1 Introduction
Objective: To introduce fundamental concepts in digital communications and
motivate the need for error correction. Also, to introduce a simple error correction
code.
Introduction
Digital communication is becoming increasing
ECE 7670
Lecture 4 Polynomials over Galois elds
Objective: To become acquainted with some basic algebraic concepts of polynomials.
1
The Euclidean algorithm
The Euclidean algorithm is perhaps the oldest algorithm in the world, being attributed to Euclid a
ECE 7670
Lecture 8 Other cyclic codes
Objective: To examine some other common families of cyclic codes
Reading:
Chapter 6.
In this chapter we will introduce some other cyclic codes which are of both
historical and practical signicance. To get started, we
ECE 771
Lecture 6 BCH and RS codes: Designer cyclic codes
Objective: We will begin with a result from linear algebra regarding Vandermonde matrices. This result is used to prove the BCH distance properties, which
will nd ways of designing codes with a sta
ECE 7670
Lecture 10 A short look at cryptography
As may be appreciated, there are several useful connections between cryptography and error control coding. Some of the algebraic techniques used in error
correction codes end up getting employed in cryptoga
ECE 7670
Lecture 7 Decoding BCH codes
Objective: We will examine several ways of nding the error locator polynomial
and using it to decode BCH or RS codes.
Reading:
Chapter 9.
1
Decoding of BCH and RS codes: the general
outline
In decoding BCH or RS code
ECE 7670
Lecture 9 Reed-Muller codes
Objective: To examine basic attributes of Reed-Muller codes
Reading:
Chapter 7.
This chapter gets us closest to the concepts of digital design for these digital
codes that we will get. We will be looking at functions
ECE 7670
Lecture 3 Groups, rings, elds, and Galois elds
Objective: To become acquainted with some basic algebraic concepts.
1
Groups
A group formalizes some of the basic rules of arithmetic necessary for cancellation
and solution of some algebraic equatio