Rank Modulation for Flash Memories

Abstract

Abstract-We explore a novel data representation scheme for multilevel flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The only allowed charge-placement mechanism is a "push-to-the-top" operation, which takes a single cell of the set and makes it the top-charged cell. The resulting scheme eliminates the need for discrete cell levels, as well as overshoot errors, when programming cells.We present unrestricted Gray codes spanning all possible n-cell states and using only "push-to-the-top" operations, and also construct balanced Gray codes. One important application of the Gray codes is the realization of logic multilevel cells, which is useful in conventional storage solutions. We also investigate rewriting schemes for random data modification. We present both an optimal scheme for the worst case rewrite performance and an approximation scheme for the average-case rewrite performance.

Gray codes over certain run-length sequences for local rank modulation

“…For exactly and efficiently representing data in flash memory, the rank modulation scheme was presented and studied in a recent series of papers, specifically [1][2][3][4]. In the rank modulation scheme [1], a permutation induced by the relative charge levels of certain cells represents stored information. In this scheme, programming operation is restricted to the "push-to-the-top" operation.…”

“…Therefore, in this scheme, over-programming (increasing the charge level of a cell above the desired amount) is not an issue. Additionally, this scheme can reduce corruption and speed up cell programming [1].…”

“…levels. Jiang et al [1] utilized a Gray code to traverse the n! states, where the transition between two adjacent states in the Gray code was facilitated by utilizing a single "pushto-the-top" operation.…”

“…In other words, by utilizing windows of size t to scan the n variables, a sequence of n/s permutations from S t is obtained in the (s, t, n)-LRM scheme. For example, if s = 1, t = 2, n = 3 and c = (0.5, 2.5, 1.5), then, by the definition of f c , f c1,2 = [2,1], f c2,3 = [1,2], f c3,1 = [1,2], and f c = ( [2,1], [1,2], [1,2]).…”

“…. , f cn−s+1,t ) ∈ R(s, t, n), a compact representation of f c may be derived by utilizing (mixed-radix) factoradic notation (see [1,17]). Specifically, for any permutation f = [f (1), .…”