Construction of MDP convolutional codes
Julia Lieb
University of Wuerzburg
Convolutional codes whose column distances increase as rapidly as possible for as long as possible are called maximum distance profile (MDP) convolutional codes. These codes are important for maximizing the error correction in sequential decoding algorithms. This is especially true for so-called reverse MDP and complete MDP convolutional codes, which have additional advantageous qualities. The existence of (reverse) MDP convolutional codes for all code parameters has already been proven. In this talk, we do the same for complete MDP convolutional codes. Moreover, we present known constructions of MDP convolutional codes and use them to derive constructions of complete MDP convolutional codes. Another crucial issue is the construction of MDP convolutional codes over fields of small size and the determination of bounds on the field size such that a construction is possible. We show that existing bounds are far away from being optimal, especially for large code rates. Finally, for some special choices for the code parameters, we give sharper bounds on the field size and construction examples for small parameters.
Julia Lieb received her Bachelor degree in Mathematics in 2012 and her Master degree in Mathematics in 2014 both from the University of Würzburg. In 2017 she obtained her PhD degree from the University of Würzburg. The topic of her thesis is in the intersection of systems theory and coding theory. In the fall term of 2016 she enjoyed a research visit at the University of Zurich. Since 2017 she is working on a project with the title "Construction of MDP convolutional codes over the erasure channel" funded by a postdoc fellowship from the University of Würzburg.