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Abstract
In this talk, we review the significant advances that have occurred in coding theory since the invention of turbo codes in 1993. To begin, we introduce turbo codes and low-density parity check (LDPC) codes (both block and convolutional), which form the basis of modern coding theory. We then discuss the role of decoding graphs in representing the iterative, probabilistic decoding algorithms used to decode these codes and show how this graph-based approach to decoding can be used to provide a unified explanation of both turbo codes and LDPC codes. Two important properties of these codes - minimum distance and iterative decoding convergence behavior - are then defined and the tradeoffs that exist between these two properties are discussed. Finally, we give a brief overview of some recent results on asymptotically good turbo and LDPC code ensembles, i.e., code ensembles for which the minimum distance grows linearly with block length as the block length tends to infinity.
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Daniel J. Costello, Jr. was born in Seattle, WA, USA, and he received his B.S.E.E. degree from Seattle University in 1964, and M.S. and Ph.D. degrees in Electrical Engineering from the University of Notre Dame, Notre Dame, IN, USA, in 1966 and 1969, respectively. In 1969 he joined the faculty of the Illinois Institute of Technology, Chicago, IL, as an Assistant Professor of Electrical Engineering. He was promoted to Associate Professor in 1973 and to Full Professor in 1980. In 1985 he became Professor of Electrical Engineering at the University of Notre Dame, Notre Dame, IN, and from 1989 to 1998 served as Chair of the Department of Electrical Engineering there. In 1991 he was selected as one of 100 Seattle University alumni to receive the Centennial Alumni Award in recognition of alumni who have displayed outstanding service to others, exceptional leadership or uncommon achievement. In 1999 he received a Humboldt Research Prize from the Alexander von Humboldt Foundation in Germany. In 2000 he was named the Leonard Bettex Professor of Electrical Engineering at Notre Dame. Prof. Costello has been a member of IEEE since 1969 and was elected Fellow in 1985. Since 1983 he has been a member of the Information Theory Society Board of Governors and in 1986 served as President of the Board. He has also served as Associate Editor for Communication Theory for the IEEE Transactions on Communications, Associate Editor for Coding Techniques for the IEEE Transactions on Information Theory, and Co-Chair of the IEEE International Symposia on Information Theory in Kobe, Japan (1988), Ulm, Germany (1997) and Chicago, IL (2004). In 2000 he was selected by the IEEE Information Theory Society as a recipient of a Third-Millennium Medal. Prof. Costello's research interests are in the area of digital communications, with special emphasis on error control coding and coded modulation. He has numerous technical publications in his field and in 1983 co-authored a textbook entitled "Error Control Coding: Fundamentals and Applications", the 2nd edition of which was published in 2004. This is the standard text in this field. Associated One-Day Workshop Mathematical Techniques in Coding TheoryThursday, 24 April 2008
Researchers from across the UK and Ireland who are interested in the
mathematics of communications and coding theory will meet on 24 April
2008 at the e-Science
Institute.
Generous support for this event was supplied by the EPSRC funded "Bridging-the-Gaps"
scheme between Engineering and Mathematics within the Edinburgh Research Partnership, the Maxwell Institute, ICMS and the e-Science Institute.
Workshop Schedule About the Maxwell
Institute Colloquia Further Links Maxwell Institute for Mathematical
Sciences University of Edinburgh School of
Mathematics Heriot-Watt University Department of
Mathematics |