EE 6344: Coding Theory

Spring 2009

Instructor	Aria Nosratinia, ECSN 4.208, Tel: 972-883-2894
Time	Mon-Wed. 5:30-6:45pm
Place	ECSN 2.126
Text	Lin and Costello, Error Control Coding, Prentice Hall, 2nd Edition
References	Wicker, Error Control Systems Prentice-hall, Cover and Thomas Elements of Information Theory John Wiley
Grading	Midterm-1 (15% - Feb. 11), Midterm-2 (25% - TBA), Final Exam (30% - 5pm Wed. May 13), Homeworks (10%), class project(s) (15%) Class participation (5%)
Other Notable Dates:	First lecture Jan. 12-- Add/drop until Jan. 20 -- Spring Break March 16-21-- Last day to drop April 7 Last lecture May 4
Prerequisite	One semester of graduate-level probability and random processes, as well as a thorough understanding of linear algebra is required. An undergraduate-level course in digital communications is recommended.
Office Hours	Mon.-Wed. 1-2pm

This course addresses the theory and application of error control coding. Error control coding is instrumental in the development of a variety of technologies, and has an irreplaceable position at the heart of digital communications. From deep-space probes to hard disks, from satellite communication to cellular telephony and CD-players, error control codes are used with virtually all transactions of digital data.

This course starts with an overview of Galois theory, and continues to cover the theory of Linear Block Codes, BCH codes, Reed-Solomon codes, convolutional codes, and trellis coded modulation. Time permitting, elements of some advanced topics will be also be presented.

Galois Theory
- Groups and GF(p) finite fields with prime p
- Generation of GF(p^m) fields
- Properties of Galois Fields
- Vector spaces over finite fields
- Polynomials over finite fields, factorization of (x^n-1)
- Rings and Ideals
Linear Block Codes
- Generator and parity check matrices
- Standard array and syndrome decoding
- Minimum distance, Error probability
- Hamming codes
- Introduction to low-density parity check (LDPC) codes
Cyclic Codes
- Description, Encoding
- Syndromes and error detection
- Decoding of cyclic codes
- Shortened cyclic codes, the CRC codes
BCH and Reed-Solomon Codes
- Binary BCH codes
- Weight distribution and error probability
- Reed-Solomon codes
- Galois Field Fourier Transform view of BCH and RS codes
- Elements of decoding algorithms
Convolutional Codes
- Structure and encoding
- The Viterbi algorithm
- Soft decision decoding
Trellis Coded Modulation
- Error control in bandlimited systems
- Set partitioning in M-ary modulations
- Ungerboeck design rules
- Decoding and performance analysis
Turbo Codes and LDPC Codes
- Introduction to turbo codes
- Iterative decoding methods
- Performance Analysis
- Tanner Graphs
- Message passing and decoding of LDPC codes
- Irregular LDPC codes, structured LDPC codes
Links related to Error Control Coding
Aria Nosratinia
Last modified: January 2009

EE 6344: Coding Theory

Spring 2009

Contents:

Links related to Error Control Coding