This paper studies the problem of reconstructing a word given several of its noisy copies. This setup is motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm, a word is transmitted over some fixed number of identical independent channels and the goal of the decoder is to output the transmitted word or some close approximation. The main focus of this paper is the case of two deletion channels and studying the error probability of the maximum-likelihood (ML) decoder under this setup. First, it is discussed how the ML decoder operates. Then, we observe that the dominant error patterns are deletions in the same run or errors resulting from alternating sequences. Based on these observations, it is derived that the error probability of the ML decoder is roughly (3q - 1)/(q - 1) p2, when the transmitted word is any q-ary sequence and p is the channel's deletion probability. We also study the cases when the transmitted word belongs to the Varshamov Tenengolts (VT) code or the shifted VT code. Lastly, the insertion channel is studied as well. These theoretical results are verified by corresponding simulations.

Flash memory is prevalent in modern servers and devices. Coupled with the scaling down of flash technology, the popularity of flash memory motivates the search for methods to increase flash reliability and lifetime. Erasures are the dominant cause of flash cell wear, but reducing them is challenging because flash is a write-once medium— memory cells must be erased prior to writing. An approach that has recently received considerable attention relies on write-once memory (WOM) codes, designed to accommodate additional writes on write-once media. However, the techniques proposed for reusing flash pages with WOM codes are limited in their scope. Many focus on the coding theory alone, whereas others suggest FTL designs that are application specific, or not applicable due to their complexity, overheads, or specific constraints of multilevel cell (MLC) flash. This work is the first that addresses all aspects of page reuse within an end-to-end analysis of a general-purpose FTL on MLC flash. We use a hardware evaluation setup to directly measure the short- and long-term effects of page reuse on SSD durability and energy consumption, and show that FTL design must explicitly take them into account. We then provide a detailed analytical model for deriving the optimal garbage collection policy for such FTL designs, and for predicting the benefit from reuse on realistic hardware and workload characteristics.

Flash memory is a write-once medium in which re-programming cells requires first erasing the block that contains them. The lifetime of the flash is a function of the number of block erasures and can be as small as several thousands. To reduce the number of block erasures, pages, which are the smallest write unit, are rewritten out-of-place in the memory. A Write-once memory (WOM) code is a coding scheme which enables to write multiple times to the block before an erasure. However, these codes come with significant rate loss. For example, the rate for writing twice (with the same rate) is at most 0.77. In this paper, we study WOM codes and their tradeoff between rate loss and reduction in the number of block erasures, when pages are written uniformly at random. First, we introduce a new measure, called erasure factor, that reflects both the number of block erasures and the amount of data that can be written on each block. A key point in our analysis is that this tradeoff depends upon the specific implementation of WOM codes in the memory. We consider two systems that use WOM codes; a conventional scheme that was commonly used, and a new recent design that preserves the overall storage capacity. While the first system can improve the erasure factor only when the storage rate is at most 0.6442, we show that the second scheme always improves this figure of merit.