Decoding convolutional codes over finite rings. A linear dynamical systems approach
Information Theory
2026-02-23 v3 math.IT
Abstract
Observable convolutional codes defined over Zpr with the Predictable Degree Property admit minimal input/state/output representations that preserve structural properties under scalar restriction. We make use of this fact to present Rosenthal's decoding algorithm for these convolutional codes. When combined with the Greferath-Vellbinger algorithm and a modified version of the Torrecillas-Lobillo-Navarro algorithm, the decoding problem of convolutional codes over Zpr reduces to selecting two decoding algorithms for linear block codes over a field. Finally, we analyze both the theoretical and practical error-correction capabilities of the combined algorithm as well as its time complexity.
Cite
@article{arxiv.2411.18316,
title = {Decoding convolutional codes over finite rings. A linear dynamical systems approach},
author = {Ángel Luis Muñoz Castañeda and Noemí Decastro-García and Miguel V. Carriegos},
journal= {arXiv preprint arXiv:2411.18316},
year = {2026}
}