Iterative Programming of Noisy Memory Cells

In this paper, we study a model, which was first presented by Bunte and Lapidoth, that mimics the programming operation of memory cells. Under this paradigm we assume that cells are programmed sequentially and individually. The programming process is modeled as transmission over a channel, while it is possible to read the cell state in order to determine its programming success, and in case of programming failure, to reprogram the cell again. Reprogramming a cell can reduce the bit error rate, however this comes with the price of increasing the overall programming time and thereby affecting the writing speed of the memory. An iterative programming scheme is an algorithm which specifies the number of attempts to program each cell. Given the programming channel and constraints on the average and maximum number of attempts to program a cell, we study programming schemes which maximize the number of bits that can be reliably stored in the memory. We extend the results by Bunte and Lapidoth and study this problem when the programming channel is either the BSC, BEC, or Z channel. For the BSC and the BEC our analysis is also extended for the case where the error probabilities on consecutive writes are not necessarily the same. Lastly, we also study a related model which is motivated by the synthesis process of DNA molecules

Iterative Programming of Noisy Memory Cells

In this paper, we study a model, which was first presented by Bunte and Lapidoth, that mimics the programming operation of memory cells. Under this paradigm we assume that cells are programmed sequentially and individually. The programming process is modeled as transmission over a channel, while it is possible to read the cell state in order to determine its programming success, and in case of programming failure, to reprogram the cell again. Reprogramming a cell can reduce the bit error rate, however this comes with the price of increasing the overall programming time and thereby affecting the writing speed of the memory. An iterative programming scheme is an algorithm which specifies the number of attempts to program each cell. Given the programming channel and constraints on the average and maximum number of attempts to program a cell, we study programming schemes which maximize the number of bits that can be reliably stored in the memory. We extend the results by Bunte and Lapidoth and study this problem when the programming channel is either the BSC, BEC, or $Z$ channel. For the BSC and the BEC our analysis is also extended for the case where the error probabilities on consecutive writes are not necessarily the same. Lastly, we also study a related model which is motivated by the synthesis process of DNA molecules.Comment: 10 pages, 2 figure

Iterative Programming of Noisy Memory Cells

In this paper, we study a model, which was first presented by Bunte and Lapidoth, that mimics the programming operation of memory cells. Under this paradigm we assume that cells are programmed sequentially and individually. The programming process is modeled as transmission over a channel, while it is possible to read the cell state in order to determine its programming success, and in case of programming failure, to reprogram the cell again. Reprogramming a cell can reduce the bit error rate, however this comes with the price of increasing the overall programming time and thereby affecting the writing speed of the memory. An iterative programming scheme is an algorithm which specifies the number of attempts to program each cell. Given the programming channel and constraints on the average and maximum number of attempts to program a cell, we study programming schemes which maximize the number of bits that can be reliably stored in the memory. We extend the results by Bunte and Lapidoth and study this problem when the programming channel is either the BSC, BEC, or Z channel. For the BSC and the BEC our analysis is also extended for the case where the error probabilities on consecutive writes are not necessarily the same. Lastly, we also study a related model which is motivated by the synthesis process of DNA molecules

Optimized Cell Programming for Flash Memories With Quantizers

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

Optimized Cell Programming for Flash Memories with Quantizers

Multi-level flash memory cells represent data by the amount of charge stored in them. Certain voltages are applied to the flash memory cells to inject charges when programming and the cell level can be only increased during the programming process as a result of the high cost of block erasures. To achieve a high speed during writing, parallel programming is used, whereby a common voltage is applied to a group of cells to inject charges simultaneously. The voltage sharing simplifies the circuitry and increases the programming speed, but it also affects the precision of charge injection and limits the storage capacity of flash memory cells. Another factor that limits the precision of cell programming is the thermal electronics noise induced in charge injection. In this paper, we focus on noiseless parallel programming of multiple cells and noisy programming of a single cell. We propose a new criterion to evaluate the performance of the cell programming which is more suitable for flash memories in practice and then we optimize the parallel programming strategy accordingly. We then proceed to noisy programming and consider the two scenarios where feedback on cell levels is either available during programming or not. We study the optimization problem under both circumstances and present algorithms to achieve the optimal performance