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In this paper, we study a model that mimics the programming operation of memory cells. This model was first introduced by Lastras-Montano et al. for continuous-alphabet channels, and later by Bunte and Lapidoth for discrete memoryless channels (DMC). Under this paradigm we assume that cells are programmed sequentially and individually. The programming process is modeled as transmission over a channel, such that 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 discrete-input memoryless symmetric channel (including the BSC,BEC, BI-AWGN) or the $Z$ 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. [ABSTRACT FROM AUTHOR]

Random I/O (RIO) codes, recently introduced by Sharon and Alrod, is a coding scheme to improve the random input/output performance of flash memories. Multilevel flash memories require, on the average, more than a single read threshold in order to read a single logical page. This number is important to be optimized since it sets the read latency of flash memories. An $(n,M,t)$ RIO code assumes that $t$ pages are stored in $n$ cells with $t+1$ levels. The first page is read by applying a read threshold between levels $t$ and $t+1$. Similarly, the second page is read by applying a read threshold between levels $t-1$ and $t$, and so on. As a consequence, if a cell reads as bit 1 for a page (say page $m$), the cell also reads as bit 1 for all the successive pages ($m+1, m+2 \cdots$). Therefore, Sharon and Alrod showed that the design of RIO codes is equivalent to the design of WOM codes. The latter family of codes attracted substantial attention in recent years in order to improve the lifetime of flash memories by allowing writing multiple messages to the memory without the need for an erase operation. In this paper, we notice two important distinctions between RIO codes and WOM codes. While in WOM codes, the messages are received one after the other and thus are not known all in advance, in RIO codes the information of all logical pages can be known in advance when programming the cells. Even though this knowledge does not improve the maximum sum-rate of RIO codes, it allows the design of efficient high-rate codes with a moderate block length, which do not exist for WOM codes. We also study another family of RIO codes, called here partial RIO codes, that allow to find even more efficient codes while allowing to sense more than a single threshold to read some pages. [ABSTRACT FROM PUBLISHER]