UCLA Extension

Introduction to Error-Control Coding

This course provides practicing engineers with an introduction to block codes, convolutional codes, trellis codes, and turbo codes.

Complete Details

For block codes:

  • BCH code design (including Reed Solomon)
  • BCH performance limits
  • Decoding algorithms (Peterson-Gorenstein-Zierler, Forney, Berlekamp-Massey, Euclidean)

For convolutional and trellis codes:

  • State diagrams and trellis diagrams
  • The Viterbi decoding algorithm
  • Determining proper traceback depth
  • Algorithms for tight bit error rate characterization

For turbo codes:

Course Materials

Lecture notes are distributed on the first day of the course. These notes are for participants only and are not for sale.

Coordinator and Lecturer

Richard D. Wesel, PhD, Associate Dean, Academic and Student Affairs, and Professor, Department of Electrical Engineering, Henry Samueli School of Engineering and Applied Science, UCLA. Since 1996, Dr. Wesel has been on the UCLA faculty pursuing research primarily in channel coding. Prior to this, he conducted research as a member of technical staff at AT&T Bell Labs. He holds four patents and has authored 100 conference and journal papers. Dr. Wesel received a National Science Foundation CAREER Award to pursue research on robust and rate-compatible coded modulation, and received an Okawa Foundation Award and the TRW Excellence in Teaching Award from the UCLA Henry Samueli School of Engineering and Applied Science. He is a Senior Member of the IEEE. He has served as chair of the Communications Major Field in the UCLA Department of Electrical Engineering and as an associate editor for the IEEE Transactions on Communications in the area of coding and coded modulation.

Daily Schedule

Day 1

Block Codes

  • Performance of block codes
  • Correction of errors and erasures
  • Hamming, Gilbert, and Singleton performance bounds
  • Performance in additive Gaussian noise
  • Understanding BCH codes
  • Cyclic codes in Galois fields
  • BCH codes and the BCH bound
  • Power method vs. polynomial method representation of Galois fields
  • Reed-Solomon Encoder
  • The Peterson-Gorenstein-Zierler Decoder
  • The Forney Algorithm
  • The Berlekamp-Massey Algorithm

Day 2

Convolutional Codes

  • Feedforward, feedback, and state-space descriptions
  • State diagrams and trellises
  • The Viterbi decoding algorithm
  • Determining free Hamming distance and minimum traceback depth

Trellis Codes

  • Combining coding and modulation
  • Set-partitioning for AWGN channels
  • Alternative architectures for fading channels
  • Viterbi decoding for trellis codes
  • Performance characterization of trellis and convolutional codes

Turbo Codes

  • Understanding turbo codes
  • Uniform interleaver analysis
  • Constituent encoder design
  • Interleaver design
  • Turbo codes for larger constellations
  • The Turbo Decoding Algorithm

Note: This course can also be offered online.

For more information contact the Short Course Program Office:
shortcourses@uclaextension.edu | (310) 825-3344 | fax (310) 206-2815