4,116 research outputs found

    New constructions of WOM codes using the Wozencraft ensemble

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    In this paper we give several new constructions of WOM codes. The novelty in our constructions is the use of the so called Wozencraft ensemble of linear codes. Specifically, we obtain the following results. We give an explicit construction of a two-write Write-Once-Memory (WOM for short) code that approaches capacity, over the binary alphabet. More formally, for every \epsilon>0, 0<p<1 and n =(1/\epsilon)^{O(1/p\epsilon)} we give a construction of a two-write WOM code of length n and capacity H(p)+1-p-\epsilon. Since the capacity of a two-write WOM code is max_p (H(p)+1-p), we get a code that is \epsilon-close to capacity. Furthermore, encoding and decoding can be done in time O(n^2.poly(log n)) and time O(n.poly(log n)), respectively, and in logarithmic space. We obtain a new encoding scheme for 3-write WOM codes over the binary alphabet. Our scheme achieves rate 1.809-\epsilon, when the block length is exp(1/\epsilon). This gives a better rate than what could be achieved using previous techniques. We highlight a connection to linear seeded extractors for bit-fixing sources. In particular we show that obtaining such an extractor with seed length O(log n) can lead to improved parameters for 2-write WOM codes. We then give an application of existing constructions of extractors to the problem of designing encoding schemes for memory with defects.Comment: 19 page

    Write-Once-Memory Codes by Source Polarization

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    We propose a new Write-Once-Memory (WOM) coding scheme based on source polarization. By applying a source polarization transformation on the to-be-determined codeword, the proposed WOM coding scheme encodes information into the bits in the high-entropy set. We prove in this paper that the proposed WOM codes are capacity-achieving. WOM codes have found many applications in modern data storage systems, such as flash memories.Comment: 5 pages, Proceedings of the International Conference on Computing, Networking and Communications (ICNC 2015), Anaheim, California, USA, February 16-19, 201

    When Do WOM Codes Improve the Erasure Factor in Flash Memories?

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    Flash memory is a write-once medium in which reprogramming 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.Comment: to be presented at ISIT 201

    Rewriting Flash Memories by Message Passing

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    This paper constructs WOM codes that combine rewriting and error correction for mitigating the reliability and the endurance problems in flash memory. We consider a rewriting model that is of practical interest to flash applications where only the second write uses WOM codes. Our WOM code construction is based on binary erasure quantization with LDGM codes, where the rewriting uses message passing and has potential to share the efficient hardware implementations with LDPC codes in practice. We show that the coding scheme achieves the capacity of the rewriting model. Extensive simulations show that the rewriting performance of our scheme compares favorably with that of polar WOM code in the rate region where high rewriting success probability is desired. We further augment our coding schemes with error correction capability. By drawing a connection to the conjugate code pairs studied in the context of quantum error correction, we develop a general framework for constructing error-correction WOM codes. Under this framework, we give an explicit construction of WOM codes whose codewords are contained in BCH codes.Comment: Submitted to ISIT 201

    Rank-Modulation Rewrite Coding for Flash Memories

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    The current flash memory technology focuses on the cost minimization of its static storage capacity. However, the resulting approach supports a relatively small number of program-erase cycles. This technology is effective for consumer devices (e.g., smartphones and cameras) where the number of program-erase cycles is small. However, it is not economical for enterprise storage systems that require a large number of lifetime writes. The proposed approach in this paper for alleviating this problem consists of the efficient integration of two key ideas: 1) improving reliability and endurance by representing the information using relative values via the rank modulation scheme and 2) increasing the overall (lifetime) capacity of the flash device via rewriting codes, namely, performing multiple writes per cell before erasure. This paper presents a new coding scheme that combines rank-modulation with rewriting. The key benefits of the new scheme include: 1) the ability to store close to 2 bit per cell on each write with minimal impact on the lifetime of the memory and 2) efficient encoding and decoding algorithms that make use of capacity-achieving write-once-memory codes that were proposed recently

    Trade-offs between Instantaneous and Total Capacity in Multi-Cell Flash Memories

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    The limited endurance of flash memories is a major design concern for enterprise storage systems. We propose a method to increase it by using relative (as opposed to fixed) cell levels and by representing the information with Write Asymmetric Memory (WAM) codes. Overall, our new method enables faster writes, improved reliability as well as improved endurance by allowing multiple writes between block erasures. We study the capacity of the new WAM codes with relative levels, where the information is represented by multiset permutations induced by the charge levels, and show that it achieves the capacity of any other WAM codes with the same number of writes. Specifically, we prove that it has the potential to double the total capacity of the memory. Since capacity can be achieved only with cells that have a large number of levels, we propose a new architecture that consists of multi-cells - each an aggregation of a number of floating gate transistors
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