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arXiv · 2411.18316

Decoding convolutional codes over finite rings. A linear dynamical systems approach

Ángel Luis Muñoz Castañeda·Noemí Decastro-García·Miguel V. Carriegos
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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.

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Ángel Luis Muñoz Castañeda, Noemí Decastro-García, Miguel V. Carriegos. 2024-11-27. Decoding convolutional codes over finite rings. A linear dynamical systems approach. https://arxiv.org/abs/2411.18316

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