Parity-check Codes from Disjunct Matrices
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909271270096896 |
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| author | Haymaker, Kathryn McMillon, Emily |
| author_facet | Haymaker, Kathryn McMillon, Emily |
| contents | The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This paper makes this connection for the first time. We provide some fundamental results on parity-check codes from general disjunct matrices (in particular, a minimum distance bound). We then consider three specific constructions of disjunct matrices and provide parameters of their corresponding parity-check codes including rate, distance, girth, and density. We show that, by choosing the correct parameters, the codes we construct have the best possible error-correction performance after one round of bit-flipping decoding with regard to a modified version of Gallager's bit-flipping decoding algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17262 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Parity-check Codes from Disjunct Matrices Haymaker, Kathryn McMillon, Emily Information Theory 94B05 (Primary) 94B25, 15B99, 05B20 (Secondary) The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This paper makes this connection for the first time. We provide some fundamental results on parity-check codes from general disjunct matrices (in particular, a minimum distance bound). We then consider three specific constructions of disjunct matrices and provide parameters of their corresponding parity-check codes including rate, distance, girth, and density. We show that, by choosing the correct parameters, the codes we construct have the best possible error-correction performance after one round of bit-flipping decoding with regard to a modified version of Gallager's bit-flipping decoding algorithm. |
| title | Parity-check Codes from Disjunct Matrices |
| topic | Information Theory 94B05 (Primary) 94B25, 15B99, 05B20 (Secondary) |
| url | https://arxiv.org/abs/2311.17262 |