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Multilevel flash memory contains blocks of cells that represent data by the amount of charge stored in them. The cell writing—or programming—process applies specified voltages in a sequential manner, injecting charge to achieve a desired level. Reducing a cell level requires a costly block erasure, so programming only increases cell levels. Parallel programming, whereby a common voltage is applied to a group of cells to inject charge simultaneously, simplifies circuitry and increases programming speed. However, cell-to-cell variations and limited programming round can adversely affect its precision. In this paper, we consider algorithms for efficient cell programming. Since cell levels are quantized to a discrete set of values, our objective is to minimize the number of cells that are not quantized to their target levels. For a specified number of programming rounds, we derive an optimal parallel programming algorithm with complexity that is polynomial in the number of cells. We extend the algorithm to account for intercell interference, where the voltage applied to a cell can affect the level of adjacent cells. We then consider noisy programming of a single cell, with and without feedback about the cell level. In both scenarios, we present an algorithm that, for a given number of programming rounds, minimizes the probability of an incorrect cell level. [ABSTRACT FROM AUTHOR]

Phase-change memory (PCM) is a promising nonvolatile solid-state memory technology. A PCM cell stores data by using its amorphous and crystalline states. The cell changes between these two states using high temperature. However, since the cells are sensitive to high temperature, it is important, when programming cells (i.e., changing cell levels), to balance the heat both in time and in space. In this paper, we study the time–space constraint for PCM, which was originally proposed by Jiang and coworkers. A code is called an (\alpha,\beta,p)-constrained code if for any \alpha consecutive rewrites and for any segment of \beta contiguous cells, the total rewrite cost of the \beta cells over those \alpha rewrites is at most p. Here, the cells are binary and the rewrite cost is defined to be the Hamming distance between the current and next memory states. First, we show a general upper bound on the achievable rate of these codes which extends the results of Jiang and coworkers. Then, we generalize their construction for (\alpha\geqslant 1,\beta=1,p=1)-constrained codes and show another construction for (\alpha=1,\beta\geqslant 1,p\geqslant 1)-constrained codes. Finally, we show that these two constructions can be used to construct codes for all values of \alpha, \beta, and p. [ABSTRACT FROM AUTHOR]