Rank-modulation rewriting codes for flash memories

Rank modulation has been recently proposed as a scheme for storing information in flash memories. Three improved aspects are disclosed. In one aspect the minimum push-up scheme, for storing data in flash memories is provided. It aims at minimizing the cost of changing the state of the memory. In another aspect, multi-cells, used for storing data in flash memories is provided. Each transistor is replaced with a multi-cell of mm transistors connected in parallel. In yet another aspect, multi-permutations, are provided. The paradigm of representing information with permutations is generalized to the case where the number of cells in each level is a constant greater than one. In yet another aspect, rank-modulation rewriting schemes which take advantage of polar codes, are provided for use with flash memory.U