Sequence Reconstruction over the Deletion Channel
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914135420174336 |
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| author | Zhu, Fengxing |
| author_facet | Zhu, Fengxing |
| contents | In this paper, we consider the Levenshtein's sequence reconstruction problem in the case where the transmitted codeword is chosen from $\{0,1\}^n$ and the channel can delete up to $t$ symbols from the transmitted codeword. We determine the minimum number of channel outputs (assuming that they are distinct) required to reconstruct a list of size $\ell-1$ of candidate sequences, one of which corresponds to the original transmitted sequence. More specifically, we determine the maximum possible size of the intersection of $\ell \geq 3$ deletion balls of radius $t$ centered at $x_1, x_2, \dots, x_{\ell}$, where $x_i \in \{0,1\}^n$ for all $i \in \{1,2,\dots,\ell\}$ and $x_i \neq x_j$ for $i \neq j$, with $n \geq t+ \ell-1$ and $t \geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequence Reconstruction over the Deletion Channel Zhu, Fengxing Information Theory Combinatorics In this paper, we consider the Levenshtein's sequence reconstruction problem in the case where the transmitted codeword is chosen from $\{0,1\}^n$ and the channel can delete up to $t$ symbols from the transmitted codeword. We determine the minimum number of channel outputs (assuming that they are distinct) required to reconstruct a list of size $\ell-1$ of candidate sequences, one of which corresponds to the original transmitted sequence. More specifically, we determine the maximum possible size of the intersection of $\ell \geq 3$ deletion balls of radius $t$ centered at $x_1, x_2, \dots, x_{\ell}$, where $x_i \in \{0,1\}^n$ for all $i \in \{1,2,\dots,\ell\}$ and $x_i \neq x_j$ for $i \neq j$, with $n \geq t+ \ell-1$ and $t \geq 1$. |
| title | Sequence Reconstruction over the Deletion Channel |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2511.01071 |