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We consider the local rank-modulation scheme in which a sliding window goingover 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 inorder to simulate conventional multi-level flash cells while retaining thebenefits of rank modulation. We provide necessary conditions for the existenceof cyclic and cyclic optimal Gray codes. We then specifically study codes ofweight 2 and upper bound their efficiency, thus proving that there are no suchasymptotically-optimal cyclic codes. In contrast, we study codes of weight 3and efficiently construct codes which are asymptotically-optimal.

Constant-Weight Gray Codes for Local Rank Modulation