The Periodicity Projection in Algebraic Decoding of Reed-Solomon Codes

Dr. Christian Senger

Institute of Communications Engineering,
Ulm University

Abstract:

Transforming received vectors from an channel in order to simplify their algebraic decoding is a well-known technique, it has been successfully applied to traditional bounded minimum distance decoders as well as modern list decoders like the Guruswami-Sudan algorithm. In literature, the technique is commonly referred to as re-encoding. Roughly speaking, the idea is to work with simple, i.e., sparse and structured, matrices or polynomials instead of dense and unstructured ones. In this talk, we present a special case of re-encoding, the so-called periodicity projection. We show that it enables certain computational savings beyond general re-encoding, which could lead to practical implementations of Guruswami-Sudan list decoding for systems with high data rates, e.g., optical transport networks.

Biography:

Christian Senger (IEEE S'05-M'11) received a diploma degree in Computer Science from Karlsruhe University (now Karlsruhe Institute of Technology) in 2006 and a Dr.-Ing. degree in Electrical Engineering from Ulm University in 2011. He is currently a postdoctoral research fellow at the Institute of Communications Engineering at Ulm University. His main fields of interest are algebraic coding techniques in general and concatenated schemes in particular.