Reed-Solomon list decoding from a system-theoretic perspective

Authors:
M. Kuijper;J. W. Polderman
Affiliations:
Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Australia;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

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.