Decoding convolutional codes over finite rings. A linear dynamical systems approach
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917283384786944 |
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| author | Castañeda, Ángel Luis Muñoz Decastro-García, Noemí Carriegos, Miguel V. |
| author_facet | Castañeda, Ángel Luis Muñoz Decastro-García, Noemí Carriegos, Miguel V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decoding convolutional codes over finite rings. A linear dynamical systems approach Castañeda, Ángel Luis Muñoz Decastro-García, Noemí Carriegos, Miguel V. Information Theory 94B10, 94B35, 93B20 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. |
| title | Decoding convolutional codes over finite rings. A linear dynamical systems approach |
| topic | Information Theory 94B10, 94B35, 93B20 |
| url | https://arxiv.org/abs/2411.18316 |