Partial rank modulation for flash memories

Rank modulation was recently proposed as an information representation for multilevel flash memories, using permutations or ranks of n flash cells. The current decoding process finds the cell with the i-th highest charge level at iteration i, for i = 1, 2, ..., n-1. Motivated by the need to reduce the number of such iterations, we consider k-partial permutations, where only the highest k cell levels are considered for information representation. We propose a generalization of Gray codes for k-partial permutations such that information is updated efficiently.