List decoding of cover metric codes up to the singleton bound
Wachter-Zeh showed that every cover metric code can be list decoded up to the Johnson-like bound. Furthermore, it was shown that the efficient list decoding of cover metric codes up to the Johnson-like bound can be performed. From the work of Wachter-Zeh, one natural question is whether the Johnson-...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2020
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| Online Access: | https://hdl.handle.net/10356/145458 |
| _version_ | 1811693273029279744 |
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| author | Liu, Shu Xing, Chaoping Yuan, Chen |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Liu, Shu Xing, Chaoping Yuan, Chen |
| author_sort | Liu, Shu |
| collection | NTU |
| description | Wachter-Zeh showed that every cover metric code can be list decoded up to the Johnson-like bound. Furthermore, it was shown that the efficient list decoding of cover metric codes up to the Johnson-like bound can be performed. From the work of Wachter-Zeh, one natural question is whether the Johnson-like bound can be improved. In this paper, we give a confirmative answer to this question by showing that the cover metric codes can be list decoded up to the Singleton bound. Our contributions consist of three parts. First, we prove that the list decodability of cover metric codes does not exceed the Singleton bound. Second, we show that, with high probability, a random cover metric code can be list decoded up to the Singleton bound, which is better than the Johnson-like bound. Third, by applying the existing decoding algorithms for Hamming metric and rank metric codes, we present explicit constructions of cover metric codes that can be efficiently list decoded up to the Singleton bound. |
| first_indexed | 2024-10-01T06:49:03Z |
| format | Journal Article |
| id | ntu-10356/145458 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:49:03Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1454582020-12-22T05:03:32Z List decoding of cover metric codes up to the singleton bound Liu, Shu Xing, Chaoping Yuan, Chen School of Physical and Mathematical Sciences Engineering::Computer science and engineering Code Decoding Wachter-Zeh showed that every cover metric code can be list decoded up to the Johnson-like bound. Furthermore, it was shown that the efficient list decoding of cover metric codes up to the Johnson-like bound can be performed. From the work of Wachter-Zeh, one natural question is whether the Johnson-like bound can be improved. In this paper, we give a confirmative answer to this question by showing that the cover metric codes can be list decoded up to the Singleton bound. Our contributions consist of three parts. First, we prove that the list decodability of cover metric codes does not exceed the Singleton bound. Second, we show that, with high probability, a random cover metric code can be list decoded up to the Singleton bound, which is better than the Johnson-like bound. Third, by applying the existing decoding algorithms for Hamming metric and rank metric codes, we present explicit constructions of cover metric codes that can be efficiently list decoded up to the Singleton bound. 2020-12-22T05:03:31Z 2020-12-22T05:03:31Z 2018 Journal Article Liu, S., Xing, C., & Yuan, C. (2018). List decoding of cover metric codes up to the singleton bound. IEEE Transactions on Information Theory, 64(4), 2410-2416. doi:10.1109/TIT.2018.2801340 1557-9654 https://hdl.handle.net/10356/145458 10.1109/TIT.2018.2801340 4 64 2410 2416 en IEEE Transactions on Information Theory © 2018 Institute of Electrical and Electronics Engineers (IEEE). All rights reserved. |
| spellingShingle | Engineering::Computer science and engineering Code Decoding Liu, Shu Xing, Chaoping Yuan, Chen List decoding of cover metric codes up to the singleton bound |
| title | List decoding of cover metric codes up to the singleton bound |
| title_full | List decoding of cover metric codes up to the singleton bound |
| title_fullStr | List decoding of cover metric codes up to the singleton bound |
| title_full_unstemmed | List decoding of cover metric codes up to the singleton bound |
| title_short | List decoding of cover metric codes up to the singleton bound |
| title_sort | list decoding of cover metric codes up to the singleton bound |
| topic | Engineering::Computer science and engineering Code Decoding |
| url | https://hdl.handle.net/10356/145458 |
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