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Abstract
Contents
Error-Correcting Codes on Graphs:
Lexicodes, Trellises and Factor Graphs
by
Ari Trachtenberg
Date:
April 28, 2001
Abstract
Acknowledgments
Contents
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
Bounding the Covering Radius
Bounding Length
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
Complexity of Min-Sum Decoding
Boolean Satisfiability
Other works
Generalized Lexicodes
Trellis-oriented G-codes
State-bounded G-Codes
Bounding decoding complexity
Tanner Graphs
Bibliography
Vita
About this document ...
http://people.bu.edu/trachten
