Weighted-Hamming Metric for Parallel Channels
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909106924683264 |
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| author | Bitzer, Sebastian Ravagnani, Alberto Weger, Violetta |
| author_facet | Bitzer, Sebastian Ravagnani, Alberto Weger, Violetta |
| contents | Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some weighted-Hamming-metric codes exhibit the unusual property that all errors beyond half the minimum distance can be corrected. Nevertheless, a tight relation between the error-correction capability of a code and its minimum distance can be established. Generalizing their Hamming-metric counterparts, upper and lower bounds on the cardinality of a code with a given weighted-Hamming distance are obtained. Finally, we propose a simple code construction with optimal minimum distance for specific parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17801 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted-Hamming Metric for Parallel Channels Bitzer, Sebastian Ravagnani, Alberto Weger, Violetta Information Theory Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some weighted-Hamming-metric codes exhibit the unusual property that all errors beyond half the minimum distance can be corrected. Nevertheless, a tight relation between the error-correction capability of a code and its minimum distance can be established. Generalizing their Hamming-metric counterparts, upper and lower bounds on the cardinality of a code with a given weighted-Hamming distance are obtained. Finally, we propose a simple code construction with optimal minimum distance for specific parameters. |
| title | Weighted-Hamming Metric for Parallel Channels |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.17801 |