Contents

(full paper available in ps or pdf)

• Abstract
• Acknowledgments
• List of Tables
• Notation
• Introduction
  • Background
    • Trellis decoding
    • Tanner graphs
  • Organization
  
  
• Lexicographic Codes
  • The lexicographic construction
    • Generalization
  • Instances of the G-construction
    • Lexicodes
    • Trellis-oriented lexicodes
    • Trellis-bounded lexicodes
  • Relation between cosets
    • Bounds on code parameters
  • Computations
  • Applications
    • Code engineering
    • Code improvement
    • Practical considerations
  • Future directions
  
  
• Tanner-Graph Decoding
  • History
  • Preliminaries
  • The structure of cycle-free codes
  • The minimum distance of cycle-free codes
    • Groundwork: auxiliary lemmas
    • Proof of the main result
  • Further results
    • Cycle-free codes and graph-theoretic codes.
    • Asymptotics for Tanner graphs with cycles
    • General Tanner graphs without cycles
  
  
• Conclusions and Future Directions
  • Trellis decoding
    • Improving the construction
    • Tanner graphs
  • Other works
  
  
• Generalized Lexicodes
  • Trellis-oriented G-codes
  • State-bounded G-Codes
  • Bounding decoding complexity
  
  
• Tanner Graphs
• Bibliography
• Vita
• About this document ...