Talk
MRD Rank Metric Convolutional Codes
Talk by Prof. Dr. Paolo A. Vettori
Speaker invited by: Prof. Dr. Joachim Rosenthal
Date: 16.05.18 Time: 16.00 - 17.00 Room: Y27H28
A rank metric code C is a set of n×m matrices over a finite field, equipped with a distance given by the rank of A-B, for any two codewords A and B. We call a code MRD (maximum rank distance) when the code distance, i.e., the minimum distance between different codewords, reaches its upper bound (depending on m, n, and the size of the code).
This kind of codes, together with an MRD construction (also known as Gabidulin code), were introduced at the end of the 70s by Delsarte. New MRD constructions were presented by various authors only in 2015, when also the first papers on rank metric convolutional codes were published: in this case, codewords are (finite) sequences of n×m matrices, usually represented as polynomial matrices.
In this talk we will generalize the notion of codeword distance to the polynomial case, establish the corresponding upper bound, construct a general family of MRD rank metric convolutional codes, and show how to decode a received message, detecting and correcting the errors that may have occurred. Finally, we will propose strategies for more efficient implementations.
Joint work with Raquel Pinto and Diego Napp (University of Aveiro) and Joachim Rosenthal (University of Zurich).