Constant-weight Gray codes for local rank modulation
Constant-weight Gray codes for local rank modulation
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DOI：
10.1109/isit.2010.5513592
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发表时间：
2010-02
期刊：
影响因子：
--
通讯作者：
Moshe Schwartz
中科院分区：
文献类型：
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作者：
Moshe Schwartz
我们考虑局部秩调制方案，其中滑动窗口经过一个序列的实值变量诱导一个序列的排列。局部秩调制作为秩调制方案的推广，最近被建议作为在闪存中存储信息的一种方式。我们研究了本地秩调制方案的恒定权重格雷码，以模拟传统的多级闪存单元，同时保留秩调制的好处。我们提供了循环和循环最佳格雷码存在的必要条件。然后，我们专门研究码的重量2和上限的效率，从而证明没有这样的渐近最优循环码。相比之下，我们研究权重为3的代码并有效地构造渐进最优的代码。
We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. The local rank-modulation, as a generalization of the rank-modulation scheme, has been recently suggested as a way of storing information in flash memory. We study constant-weight Gray codes for the local rank-modulation scheme in order to simulate conventional multi-level flash cells while retaining the benefits of rank modulation. We provide necessary conditions for the existence of cyclic and cyclic optimal Gray codes. We then specifically study codes of weight 2 and upper bound their efficiency, thus proving that there are no such asymptotically-optimal cyclic codes. In contrast, we study codes of weight 3 and efficiently construct codes which are asymptotically-optimal.