Gray codes over certain run-length sequences for local rank modulation  

作　　者：Xiang WANG Fang-Wei FU 

机构地区：[1]National Computer Network Emergency Response Technical Team, Beijing 100029, China [2]The Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China

出　　处：《Science China(Information Sciences)》2018年第10期94-109,共16页中国科学（信息科学）（英文版）

基　　金：supported by National Basic Research Program of China (973) (Grant No. 2013CB834204);National Natural Science Foundation of China (Grant No. 61571243)

摘　　要：In the local rank modulation （LRM） scheme, a sliding window produces a sequence of permu-tations by moving over a sequence of variables. LRM has been presented as a method of storing data inflash memory, which represents a natural generalization of the classical rank modulation scheme. In thispaper, we present a study on Gray codes over certain run-length sequences for the （1, 2, n）-LRM scheme tosimulate virtual multilevel flash memory cells while maintaining the advantages of LRM. Unlike previousstudies on the LRM scheme, we present Gray codes over certain run-length sequences in the （1, 2, n）-LRMscheme. This class of Gray codes can overcome the drawback of the many distinct charge levels requiredin the rank modulation scheme and in certain Gray codes for LRM. Furthermore, we demonstrate that theproposed codes have an asymptotically optimal rate.In the local rank modulation （LRM） scheme, a sliding window produces a sequence of permu-tations by moving over a sequence of variables. LRM has been presented as a method of storing data inflash memory, which represents a natural generalization of the classical rank modulation scheme. In thispaper, we present a study on Gray codes over certain run-length sequences for the （1, 2, n）-LRM scheme tosimulate virtual multilevel flash memory cells while maintaining the advantages of LRM. Unlike previousstudies on the LRM scheme, we present Gray codes over certain run-length sequences in the （1, 2, n）-LRMscheme. This class of Gray codes can overcome the drawback of the many distinct charge levels requiredin the rank modulation scheme and in certain Gray codes for LRM. Furthermore, we demonstrate that theproposed codes have an asymptotically optimal rate.

关 键 词：flash memory local rank modulation Gray codes rank modulation run-length sequences 

分 类 号：TP333[自动化与计算机技术—计算机系统结构]