论文标题
改进的置换和多损点代码纠正稳定缺失爆发的构造
Improved constructions of permutation and multi-permutation codes correcting a burst of stable deletions
论文作者
论文摘要
由于它们的各种应用，尤其是在闪存中，因此已广泛考虑了置换代码和多重代码。在本文中，我们将置换代码和多损点代码视为稳定缺失。特别是，我们提出了置换代码的构造，以纠正长度$ s $的突发稳定删除，并带有冗余$ \ log n+ 2 \ log \ log \ log \ log n+ o（1）$。与先前的已知结果相比，我们的改进依赖于不同的策略来检索排列阵列表示的第一行中缺少符号。我们还将构造概括为多渗透和可变长度突发模型。此外，我们提出了一个线性时间编码器，具有最佳冗余，用于单个稳定删除校正置换代码。
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.
