Decoding of Space-Symmetric Rank Errors

Thomas Jerkovits, Vladimir Sidorenko, Antonia Wachter-Zeh

Abstract: This paper investigates the decoding of certain Gabidulin codes over a channel with space-symmetric errors. Space-symmetric errors are additive error matrices that have the property that their column and row spaces are equal. We show that for channels restricted to space-symmetric errors, with high probability errors of rank up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2 (n-k)/3$</tex> can be decoded with a Gabidulin code of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> and dimension <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> , using a weak-self orthogonal basis as code locators.