136 research outputs found
Fast Encoding and Decoding of Gabidulin Codes
Gabidulin codes are the rank-metric analogs of Reed-Solomon codes and have a
major role in practical error control for network coding. This paper presents
new encoding and decoding algorithms for Gabidulin codes based on
low-complexity normal bases. In addition, a new decoding algorithm is proposed
based on a transform-domain approach. Together, these represent the fastest
known algorithms for encoding and decoding Gabidulin codes.Comment: 5 pages, 1 figure, to be published at ISIT 200
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-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
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