Coding for Storage and Networks: Decoding of Crisscross Errors

Dr. Antonia Wachter-Zeh

Technion – Israel Institute of Technology, Haifa, Israel

Abstract:

Reliable data storage and data transmission has become an every-day goal. Crisscross errors occur frequently in data storage systems and networks. In this talk, list decoding of crisscross errors in arrays over finite fields is considered. For this purpose, the so- called cover metric is used, where the cover of a matrix is a set of rows and columns which contains all non-zero elements of the matrix. A Johnson-like upper bound on the maximum list size in the cover metric is derived, showing that the list of codewords has polynomial size up to a certain radius. Further, a simple list decoding algorithm for a known optimal code construction is presented, which decodes errors in the cover metric up to our upper bound. These results reveal significant differences between the cover metric and the rank metric. Finally, possible future research directions are outlined.

Biography:

Antonia Wachter-Zeh received an equivalent of the B.Sc. degree in electrical engineering in 2007 from the University of Applied Science Ravensburg, Germany, and the M.Sc. degree in communications technology in 2009 from Ulm University, Germany. She obtained her Ph.D. degree in 2013 at the Institute of Communications Engineering, University of Ulm, Germany and at the Institut de recherche mathématique de Rennes (IRMAR), Université de Rennes 1, Rennes, France. Her dissertation deals with block and convolutional codes in rank metric. Currently, she is a postdoctoral researcher at the Technion—Israel Institute of Technology, Haifa, Israel. Her research interests are coding and information theory and their application to storage and networks.