4,336 research outputs found
Systems theoretic methods in decoding
In this paper we show how ideas based on system theoretic modeling of linear behaviors may be used for decoding of linear codes. In particular we show how Sudan's bivariate interpolation approach to list decoding of RS codes allows a system theoretic interpretation
Gr\"obner Bases for Linearized Polynomials
In this work we develop the theory of Gr\"obner bases for modules over the
ring of univariate linearized polynomials with coefficients from a finite
field
Iterative List-Decoding of Gabidulin Codes via Gr\"obner Based Interpolation
We show how Gabidulin codes can be list decoded by using an iterative
parametrization approach. For a given received word, our decoding algorithm
processes its entries one by one, constructing four polynomials at each step.
This then yields a parametrization of interpolating solutions for the data so
far. From the final result a list of all codewords that are closest to the
received word with respect to the rank metric is obtained.Comment: Submitted to IEEE Information Theory Workshop 2014 in Hobart,
Australi
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