Compressed Rank Modulation

We propose a generalization of Rank Modulation (RM) scheme, Compressed Rank Modulation (CRM) scheme for nonvolatile memories. CRM stores information in the multiset permutation induced by the charge levels of N = ⁿΣ_i=1 m_i cells: set the ranks of the first m₁ highest charge level cells as 1, the ranks of the next m₂ highest charge level cells are 2, and the ranks of the last m_n highest charge level cells are n. The only allowed charge-placement method is the minimal-push-up aiming to minimize the increase of highest charge levels, and such minimization of highest charge level increase is defined as rewriting cost. CRM achieves a higher capacity comparing with RM, and maintains its advantages meanwhile. The closed-form formula for rewriting cost, sizes of balls, asymptotical rate analysis for rewriting codes, and one rewriting code construction are presented.