Multi-permutation codes for rank modulation scheme have been recently proposed for efficiently storing data in flash memories. In this letter, we investigate the problem of a single burst unstable deletion (BUD) of length $t$ in a $t$ -balanced multi-permutation and this problem can be decomposed into the sub-problems of a single permutation-invariant deletion (PID) in $t$ permutations by a rank demodulation method. Based on the rank demodulation method and the interleaving of $t$ single-PID-correcting permutation codes, we construct two classes of $t$ -balanced multi-permutation codes that are capable of correcting a single BUD of length $t$ . Moreover, the constructed codes can achieve higher rates compared with the existing code. The decoding methods are provided in the proofs and verified by some examples.

中文翻译：

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纠正闪存中单次突发不稳定删除的多排列代码

最近已经提出了用于秩调制方案的多置换码以在闪存中有效地存储数据。在这封信中，我们研究了单次突发不稳定缺失 (BUD) 长度的问题 $t$ 在一个 $t$ -平衡多排列，这个问题可以分解为单个排列不变删除（PID）的子问题 $t$ 通过秩解调方法进行排列。基于秩解调方法和交织 $t$ 单PID校正置换码，我们构造了两类 $t$ - 平衡多置换码，能够纠正单个长度的 BUD $t$ . 此外，与现有代码相比，构建的代码可以实现更高的速率。证明中提供了解码方法，并通过一些例子进行了验证。