A module minimization approach to Gabidulin decoding via interpolation

Abstract

Abstract:We focus on iterative interpolation-based decoding of Gabidulin codes and present an algorithm that computes a minimal basis for an interpolation module. We extend existing results for Reed-Solomon codes in showing that this minimal basis gives rise to a parametrization of elements in the module that lead to all Gabidulin decoding solutions that are at a fixed distance from the received word. Our module-theoretic approach strengthens the link between Gabidulin decoding and Reed-Solomon decoding, thus providing a basis for further work into Gabidulin list decoding.2010 MSC: 11T71, 94B35

Randomized Decoding of Gabidulin Codes Beyond the Unique Decoding Radius

“…However, there is no upper bound on the list size and the complexity of the decoding algorithm. In future work, the algorithm from [16] should be adapted to solve Problem 2 which could allow for estimating the complexity of the resulting algorithm.…”

“…There is a list decoding algorithm for Gabidulin codes based on Gröbner bases that allows to correct errors beyond the unique decoding radius [16]. However, there is no upper bound on the list size and the complexity of the decoding A Proof of Lemma 1…”

“…838.54 2 504.70 2 410.92algorithm. In future work, the algorithm from[16] should be adapted to solve Problem 2 which could allow for estimating the complexity of the resulting algorithm.32. Wachter-Zeh, A.: Decoding of block and convolutional codes in rank metric.…”