Institute of Mathematics

Talk

Modul:   MAT076  Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

New Algebraic Construction of MDP Convolutional Codes

Gianira Nicoletta Alfarano talk

Date: 11.12.19  Time: 16.15 - 17.15  Room:

Convolutional codes were introduced in 1955 by Peter Elias, as an interesting natural generalization of classical block codes and they have been widely implemented in practice with applications in mobile communications, satellite communications, and data streaming. Unfortunately, there exist very few algebraic general constructions of convolutional codes and most of the existing ones that have good designed distance have been found by computer search. The algebraic construction of convolutional codes with a large distance that admits an efficient decoding algorithm by exploiting the algebraic structure of the code remains a big open problem in the area. In this talk, we introduce a new algebraic construction of a class of convolutional codes. Since these codes are built upon generalized Vandermonde matrices, they can be seen as an extension of Reed-Solomon (RS) block codes to the context of convolutional codes. For this reason, we will refer to them as Weighted RS convolutional codes. We will discuss the MDP property of these codes and we will give some asymptotic results on the field size that they require to be built. Finally, we will give a comparison with the existing constructions.