Improved constructions of permutation and multi-permutation codes correcting a burst of stable deletions

Yubo Sun; Yiwei Zhang; Gennian Ge

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arXiv · 2208.10110

Improved constructions of permutation and multi-permutation codes correcting a burst of stable deletions

Yubo Sun·Yiwei Zhang·Gennian Ge

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Abstract

Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable deletions. In particular, we propose a construction of permutation codes correcting a burst stable deletion of length $s$, with redundancy $\log n+ 2\log \log n+O(1)$. Compared to the previous known results, our improvement relies on a different strategy to retrieve the missing symbol on the first row of the array representation of a permutation. We also generalize our constructions for multi-permutations and the variable length burst model. Furthermore, we propose a linear-time encoder with optimal redundancy for single stable deletion correcting permutation codes.

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Yubo Sun, Yiwei Zhang, Gennian Ge. 2022-08-22. Improved constructions of permutation and multi-permutation codes correcting a burst of stable deletions. https://arxiv.org/abs/2208.10110

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