Heisenberg-Weyl groups and their application to sequence design

  • Date: 07/18/2006

Robert Calderbank (Princeton University)


Simon Fraser University


We will describe how Heisenberg-Weyl groups appear in the construction
of phase coded radar waveforms, in the design of spreading sequences
in wireless communications, and in the theory of classical and quantum
error-correcting codes. Interesting examples include the first and
second order Reed-Muller codes, the binary and quaternary Kerdock codes,
and the Welti and other Golay complementary sequences. These talks
will focus on sequences contained in orthonormal bases fixed by maximal
abelian subgroups of the Heisenberg-Weyl group. We will describe how
the correlation properties of sequences in these orthonormal bases
are determined by the symmetry group of the basis in the Heisenberg-Weyl


Robert Calderbank is currently a
professor in the Department of
Electrical Engineering at
Princeton University. Prof.
Calderbank's inventions have
transformed communications
practice in voice-band modems,
and advanced read channels for
magnetic recording and wireless
systems. He and Peter Shor created
the framework for fault-tolerant quantum computing.
He was awarded the IEEE Information
Theory Prize Paper Award in 1995 for his work on
the Z4-linearity of Kerdock and Preparata codes, and
again in 1999 for the invention of space-time codes.
Prof. Calderbank received the IEEE Millenium
Medal in 2000, and was elected to the National
Academy of Engineering in 2005. Prior to joining
Princeton, Prof. Calderbank was a Vice President
for research at AT&T, where he had worked for over
20 years. He was appointed an AT&T Fellow in 2000.

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