List decodability of symbol-pair codes
We investigate the list decodability of symbol-pair codes 1 in this paper. First, we show that the list decodability of every symbol-pair code does not exceed the Gilbert-Varshamov bound. On the other hand, we are able to prove that with high probability, a random symbol-pair code can be list decode...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/138021 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | We investigate the list decodability of symbol-pair codes 1 in this paper. First, we show that the list decodability of every symbol-pair code does not exceed the Gilbert-Varshamov bound. On the other hand, we are able to prove that with high probability, a random symbol-pair code can be list decoded up to the Gilbert-Varshamov bound. Our second result of this paper is to derive the Johnson-type bound, i.e., a lower bound on list decoding radius in terms of minimum distance. Finally, we present a list decoding algorithm of Reed-Solomon codes beyond the Johnson-type bound in the pair metric. 1 A symbol-pair code is referred to a code in the pair metric. |
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