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Prof.-em. Dr. James L. Massey*The Swiss Federal Institute of Technology (ETH), ZürichAdjunct Professor, Lund University, Sweden Adjunct Professor, Technical University of Denmark |
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Feedback, Erasures, Zero-Errors, and
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Claude E. Shannon devoted the inaugural "Shannon Lecture" at the 1973 IEEE
International Symposium on Information Theory (ISIT) to the role of feedback in
communications, implicitly challenging other information theorists to get to
work on this topic. Peter Elias based his Shannon Lecture at the 1977 ISIT on
the binary erasure channel (in which a transmitted binary digit is either
received error-free or as an erasure symbol), which he described as the
simplest channel that incorporates the essential features of "noisiness". Our
aim in this lecture is to take up Shannon's challenge by following Elias's
suggestion that the binary erasure channel is a good place to start. We will
be led naturally to consider data transmission systems that yield zero-errors,
i.e., not just a low probability of error but no errors at all. Shannon
already in 1956 defined the zero-error capacity of a channel as the upper limit
of rates at which zero-error transmission is possible, but paradoxes that occur
when this definition is applied to the binary erasure channel will force us to
expand this concept. Elias in 1955 introduced infinite-constraint-length codes
in a paper that gave birth to "convolutional codes". We find that new
paradoxes occur for zero-error transmission when infinite-constraint-length
codes are allowed. Resolving all these paradoxes leads to a taxonomy of
channels in which the binary erasure channel occupies a prominent place.
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| Thursday, January 26, 2006 4:00p.m. - McMurtry Auditorium, Anne and Charles Duncan Hall Rice University |
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Sponsored by: Electrical and Computer Engineering Department Host: A.C. Antoulas, (713) 348-5132, aca@rice.edu
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Comments and questions to:
www-ece@ece.rice.edu
Last modified: December 5, 2005