Alfarano, Gianira N., Napp, Diego, Neri, Alessandro, Requena Arévalo, Verónica
Weighted Reed–Solomon convolutional codes
Linear and Multilinear Algebra. 2024, 72(5): 841-874. https://doi.org/10.1080/03081087.2023.2169232
URI: http://hdl.handle.net/10045/141444
DOI: 10.1080/03081087.2023.2169232
ISSN: 0308-1087 (Print)
Abstract: 
In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed–Solomon block codes to the context of convolutional codes. For this reason we call them weighted Reed–Solomon (WRS) convolutional codes. We show that under some constraints on the defining parameters these codes are Maximum Distance Profile (MDP), which means that they have the maximal possible growth in their column distance profile. We study the size of the field needed to obtain WRS convolutional codes which are MDP and compare it with the existing general constructions of MDP convolutional codes in the literature, showing that in many cases WRS convolutional codes require significantly smaller fields.
Keywords:MDP convolutional codes, Vandermonde matrices, Weighted Reed–Solomon convolutional codes
Taylor & Francis
info:eu-repo/semantics/article