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Rank modulation has been recently proposed as a scheme for storing information in flash memories. While rank modulation has advantages in improving write speed and endurance, the current encoding approach is based on the "Push to the top" operation that is not efficient in the general case. The authors propose a new encoding procedure where a cell level is raised to be higher than the minimal necessary subset -instead of all - of the other cell levels. This new procedure leads to a significantly more compressed (lower charge levels) encoding. They derive an upper bound for a family of codes that utilize the proposed encoding procedure, and consider code constructions that achieve that bound for several special cases.
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