768 research outputs found
Efficient Interpolation in the Guruswami-Sudan Algorithm
A novel algorithm is proposed for the interpolation step of the
Guruswami-Sudan list decoding algorithm. The proposed method is based on the
binary exponentiation algorithm, and can be considered as an extension of the
Lee-O'Sullivan algorithm. The algorithm is shown to achieve both asymptotical
and practical performance gain compared to the case of iterative interpolation
algorithm. Further complexity reduction is achieved by integrating the proposed
method with re-encoding. The key contribution of the paper, which enables the
complexity reduction, is a novel randomized ideal multiplication algorithm.Comment: Submitted to IEEE Transactions on Information Theor
Reed-Solomon list decoding from a system-theoretic perspective
In this paper, the Sudan-Guruswami approach to list decoding of Reed-Solomon (RS) codes is cast in a system-theoretic framework. With the data, a set of trajectories or time series is associated which is then modeled as a so-called behavior. In this way, a connection is made with the behavioral approach to system theory. It is shown how a polynomial representation of the modeling behavior gives rise to the bivariate interpolating polynomials of the Sudan-Guruswami approach. The concept of "weighted row reduced" is introduced and used to achieve minimality. Two decoding methods are derived and a parametrization of all bivariate interpolating polynomials is given
Prefactor Reduction of the Guruswami-Sudan Interpolation Step
The concept of prefactors is considered in order to decrease the complexity
of the Guruswami-Sudan interpolation step for generalized Reed-Solomon codes.
It is shown that the well-known re-encoding projection due to Koetter et al.
leads to one type of such prefactors. The new type of Sierpinski prefactors is
introduced. The latter are based on the fact that many binomial coefficients in
the Hasse derivative associated with the Guruswami-Sudan interpolation step are
zero modulo the base field characteristic. It is shown that both types of
prefactors can be combined and how arbitrary prefactors can be used to derive a
reduced Guruswami-Sudan interpolation step.Comment: 13 pages, 3 figure
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