ECE 590.10: Error Correcting Codes

Course Information

• Syllabus (updated 03/28/25)
  

  • Lecture: 1:25 - 2:40 TTH @ Hudson Hall 218
    

  • Instructors: Henry Pfister (henry.pfister@duke.edu) and Hanwen Yao (hanwen.yao@duke.edu)

• Required Textbooks

  • Error Correction Coding: Mathematical Methods and Algorithms by Todd K. Moon
    

• Supplemental Textbooks

  • Algebraic Codes for Data Transmission by Richard E. Blahut
    

  • Error Control Coding by Shu Lin and Daniel J. Costello
    

  • Finite Fields for Computer Scientists and Engineers by Robert J. McEliece
    

Course Notes

Background

• Mathematical Prerequisites
  

• Python Coding Examples
  

Basic Coding

• Introduction to Coding
  

• Bounds on Code Parameters

• Reed-Muller Codes

• Code Symmetry and Reed-Muller Codes

• Introduction to Reed-Solomon Codes

• Maximum-Likelihood Performance

• Maximum-Likelihood Slides

Graphical Representations of Codes

• Graphical Representation Notes

• Graphical Representation Slides

• LDPC Codes, Factor Graphs, and Belief Propagation

• Density Evolution Handout
  

Cyclic, Reed-Solomon, and BCH Codes

• Cyclic Code Notes

• Cyclic Code Slides

• Finite Fields and Double Error Correction
  

• The Structure of Finite Fields
  

• Algebraic Decoding of Reed-Solomon and BCH Codes
  

Quantum Error Correction

Polar Codes

• Polar Codes Handout
  

• Polar Codes Slides
  

Handouts

• Homework 0 (not graded)
  

• Homework 1

• Homework 2
  

Supplemental Course Notes

• Peeling Decoder Handout
  

• EXIT Area Theorem Handout
  

• Martingale Handout
  

Coding Theory on Wikipedia

Coding Theory , Hamming Distance , Singleton Bound , Hamming Bound , Gilbert-Varshamov Bound
Finite Field , Linear Code , Linear Feedback Shift Register , Convolutional Code , de Bruijn Graph

Abstract Algebra on Wikipedia

Group , Cyclic Group , Dihedral Group , Direct Product , Subgroup , Coset, Lagrange's Theorem
Normal Subgroup , Homomorphism , Quotient Group , Ring , Polynomial Ring , Ideal , Quotient Ring
Field , Finite Field , Vector Space , Basis , Rank of a Matrix , Determinant , Formal Power Series
Generating Function

Other Books, Papers, and Web Resources

Coding Theory

• How to Compute Weight Enumerators of Convolutional Codes (very nice tutorial by McEliece)
  

• Low-Density Parity-Check Codes by Gallager
  

• A Recursive Approach to Low Complexity Codes by Tanner
  

• Efficient Erasure Codes by Luby et al.
  

• The Capacity of Low-Density Parity-Check Codes under Message-Passing Decoding by Richardson and Urbanke
  

• Deterministic Constructions for Large Girth Protograph LDPC Codes by Pradhan, Subramanian, and Thangaraj
  

• Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels by Arikan
  

• Introduction to Polar Codes by Mori
  

• Systematic Polar Coding by Arikan

Factor Graphs

• The Generalized Distributive Law (a unification of many algorithms by Aji and McEliece)
  

• Partition Functions of Normal Factor Graphs by Forney and Vontobel
  

• Codes on Graphs: Duality and MacWilliams Identities by Forney
  

Linear Programming Decoding

• Using Linear Programming to Decode Binary linear Codes by Feldman, Karger, and Wainwright
  

• Graph-Cover Decoding and Finite-Length Analysis of Message-Passing Iterative Decoding of LDPC Codes by Vontobel and Koetter
  

• Decomposition Methods for Large Scale LP Decoding by Barman et al.
  

• Exploiting Parity-Polytope Geometry in Approximate and Randomized Scheduled ADMM-LP Decoding by Asadzadeh, Ho, Kschischang, and Draper