1,626 research outputs found
List-Decoding Gabidulin Codes via Interpolation and the Euclidean Algorithm
We show how Gabidulin codes can be list decoded by using a parametrization
approach. For this we consider a certain module in the ring of linearized
polynomials and find a minimal basis for this module using the Euclidean
algorithm with respect to composition of polynomials. For a given received
word, our decoding algorithm computes a list of all codewords that are closest
to the received word with respect to the rank metric.Comment: Submitted to ISITA 2014, IEICE copyright upon acceptanc
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
List and Unique Error-Erasure Decoding of Interleaved Gabidulin Codes with Interpolation Techniques
A new interpolation-based decoding principle for interleaved Gabidulin codes
is presented. The approach consists of two steps: First, a multi-variate
linearized polynomial is constructed which interpolates the coefficients of the
received word and second, the roots of this polynomial have to be found. Due to
the specific structure of the interpolation polynomial, both steps
(interpolation and root-finding) can be accomplished by solving a linear system
of equations. This decoding principle can be applied as a list decoding
algorithm (where the list size is not necessarily bounded polynomially) as well
as an efficient probabilistic unique decoding algorithm. For the unique
decoder, we show a connection to known unique decoding approaches and give an
upper bound on the failure probability. Finally, we generalize our approach to
incorporate not only errors, but also row and column erasures.Comment: accepted for Designs, Codes and Cryptography; presented in part at
WCC 2013, Bergen, Norwa
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