Weight-2 input sequences of 1/n convolutional codes from linear systems point of view
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http://hdl.handle.net/10045/128552
| Títol: | Weight-2 input sequences of 1/n convolutional codes from linear systems point of view |
|---|---|
| Autors: | Herranz, Victoria | Napp, Diego | Perea, Carmen |
| Grups d'investigació o GITE: | Grupo de Álgebra y Geometría (GAG) |
| Centre, Departament o Servei: | Universidad de Alicante. Departamento de Matemáticas |
| Paraules clau: | Convolutional codes | Input-state-output representations | Linear time-invariant systems | Effective free distance |
| Data de publicació: | 11-d’octubre-2022 |
| Editor: | AIMS Press |
| Citació bibliogràfica: | AIMS Mathematics. 2023, 8(1): 713-732. https://doi.org/10.3934/math.2023034 |
| Resum: | Convolutional codes form an important class of codes that have memory. One natural way to study these codes is by means of input state output representations. In this paper we study the minimum (Hamming) weight among codewords produced by input sequences of weight two. In this paper, we consider rate 1/n and use the linear system setting called (A,B,C,D) input-state-space representations of convolutional codes for our analysis. Previous results on this area were recently derived assuming that the matrix A, in the input-state-output representation, is nonsingular. This work completes this thread of research by treating the nontrivial case in which A is singular. Codewords generated by weight-2 inputs are relevant to determine the effective free distance of Turbo codes. |
| Patrocinadors: | The research of the second author was supported by Spanish I+D+i project PID2019-108668GB-I00 of MCIN/AEI/10.13039/501100011033. |
| URI: | http://hdl.handle.net/10045/128552 |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2023034 |
| Idioma: | eng |
| Tipus: | info:eu-repo/semantics/article |
| Drets: | © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0) |
| Revisió científica: | si |
| Versió de l'editor: | https://doi.org/10.3934/math.2023034 |
| Apareix a la col·lecció: | INV - GAG - Artículos de Revistas |
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| Arxiu | Descripció | Tamany | Format | |
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 Herranz_etal_2022_AIMSMath.pdf | 274,81 kB | Adobe PDF | Obrir Vista prèvia | |
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