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Contact:
Marcus Greferath
School of Math. Sciences
University College Dublin
Belfield, Dublin 4, Ireland
Phone:
+353-1-716-2588 (UCD)
+353-85-153-0951 (mobile)
Joachim Rosenthal
Institut of Mathematics
University of Zurich
Winterthurerstrasse 190
8057 Zurich, Switzerland
Phone:
+41-44-63 55884 (office)
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ITW 2010 Dublin
IEEE Information Theory Workshop
Dublin, August 30 - September 3, 2010
Algebraic codes
Tue 31 Aug, 14.40-16.00, Room 3
Contributed session
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Eeva Suvitie and Jyrki Lahtonen
On the Degree of the Inverse of Quadratic Permutation Polynomial Interleavers
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Abstract:
An integral component of a turbo code is a carefully designed
interleaver. Interleavers based on quadratic permutation
polynomials (modulo N) were introduced by Sun and Takeshita. They
have several good properties and were selected to be used in a
future cellular phone system. Ryu and Takeshita later initiated the
study of the related deinterleavers. Here we extend this latter work
and introduce a very efficient method for computing the (degree of
the) lowest degree polynomial giving the deinterleaver. Our approach
is based on combining two techniques. The Chinese remainder theorem
allows us to study one prime factor of N at a time. Our other
technique is to first present the inverse function as a power
series, and then turn that power series to a low degree polynomial
using a Gröbner basis of the ideal of polynomials vanishing modulo a
prime power.
Tue 31 Aug, 14.40-15.00, Room 3
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M. M. Nastasescu and A. R. Calderbank
The Projective Kerdock Code
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Abstract:
Certain nonlinear binary codes can be constructed as
binary images of Z4-linear codes under the Gray map. Examples
include the second-order Reed-Muller code and the Kerdock and
Preparata codes. In this paper, we consider a new quaternary code
which is an additive subcode of the Z4-linear Kerdock code. The
Kerdock code is the direct sum of a one-dimensional quaternary code
and the quaternary subcode examined in this paper. This paper
calculates the weight distribution of the projective Kerdock code
from which the weight distribution of the dual code can be
computed. The dual code is a supercode of the quaternary Preparata
code. The projective Kerdock code is used to construct a
deterministic measurement matrix for compressed sensing. Numerical
experiments are presented for sparse reconstruction using the LASSO
that show improvement over random Gaussian matrices of the same
size.
Tue 31 Aug, 15.00-15.20, Room 3
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José Joaquín Bernal and Juan Jacobo Simón
Information sets for abelian codes
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Tue 31 Aug, 15.20-15.40, Room 3
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Joaquim Borges, Cristina Fernández-Córdoba, and Steven T. Dougherty
Additive Codes over Z2 x Z4
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Abstract:
We describe recent results for codes over Z2 x Z4 giving
their connection to binary codes via a natural Gray map. We study
Z2Z4 self-dual codes and we state the major results concerning
these codes. We state several open questions and discuss possible
avenues of research.
Tue 31 Aug, 15.40-16.00, Room 3
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