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Error Control Schemes for Modern Flash Memories: Solutions for Flash deficiencies

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Abstract

Flash, already one of the dominant forms of data storage for mobile consumer devices, such as smartphones and media players, is experiencing explosive growth in cloud and enterprise applications. Flash devices offer very high access speeds, low power consumption, and physical resiliency. Our goal in this article is to provide a high-level overview of error correction for Flash. We will begin by discussing Flash functionality and design. We will introduce the nature of Flash deficiencies. Afterwards, we describe the basics of ECCs. We discuss BCH and LDPC codes in particular and wrap up the article with more directions for Flash coding.

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... As for the long term, charge leakage may be one of critical issues of multi-level cell memories. As documented in [8][9][10][11][12][13], voltage of a cell decreases and some cells even become defective over time. The amount of charge leakage, which can be modeled as gain and/or offset mismatch, depends on various physical parameters, such as the device 1. INTRODUCTION temperature, the magnitude of the charge, and the time elapsed between writing and reading data [11]. ...
... As documented in [8][9][10][11][12][13], voltage of a cell decreases and some cells even become defective over time. The amount of charge leakage, which can be modeled as gain and/or offset mismatch, depends on various physical parameters, such as the device 1. INTRODUCTION temperature, the magnitude of the charge, and the time elapsed between writing and reading data [11]. Importantly, the charge leakage leads to a severe shift in the voltage distribution over time. ...
... There are many examples of channels with offset and gain mismatch. Reading errors in Flash memories may originate from cell drift in aging devices [11]. In the digital optical recording, fingerprints and scratches on the surface of discs result in offset variations of the retrieved signal [65]. ...
... While noise may vary from symbol to symbol, it is often assumed that the offset is constant within a block of symbols. For example, charge leakage from memory cells may cause such an offset of the stored signal values [12]. While Euclidean distance based decoders are known to be optimal if the transmitted or stored signal is only disturbed by Gaussian noise, they may perform badly if there is offset as well. ...
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Decoders minimizing the Euclidean distance between the received word and the candidate codewords are known to be optimal for channels suffering from Gaussian noise. However, when the stored or transmitted signals are also corrupted by an unknown offset, other decoders may perform better. In particular, applying the Euclidean distance on normalized words makes the decoding result independent of the offset. The use of this distance measure calls for alternative code design criteria in order to get good performance in the presence of both noise and offset. In this context, various adapted versions of classical binary block codes are proposed, such as (i) cosets of linear codes, (ii) (unions of) constant weight codes, and (iii) unordered codes. It is shown that considerable performance improvements can be achieved, particularly when the offset is large compared to the noise.
... These techniques incorporate redundant resources (e.g., spare columns and spare blocks, etc.) to replace the detected faulty cells. Besides these spare-based techniques, error-correction code (ECC) is also considered as the most popular and cost-effective method [4,11,15,21,22,25,27] for repairing flash memories by incorporating check bits for locating and correcting faulty bits. Two popularly used ECC techniques include the Bose-Chaudhuri-Hocquenghem (BCH) code [14] and the Hamming code [7]. ...
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... In general, we can say that dealing with varying offset and/or gain is an important issue in signal processing for modern storage and communication systems. For example, methods to solve these difficulties in flash memories have been discussed in, e.g., [3], [4], and [5]. Also, in optical disc media, the retrieved signal depends on the dimensions of the written features and upon the quality of the light path, which may be obscured by fingerprints or scratches on the substrate, leading to offset and gain variations of the retrieved signal. ...
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... Dealing with rapidly varying offset and/or gain is an important issue in signal processing for modern storage and communication systems. For example, methods to solve these difficulties in Flash memories have been discussed in, e.g., [7], [9], and [11]. Also, in optical disc media, the retrieved signal depends on the dimensions of the written features and upon the quality of the light path, which may be obscured by fingerprints or scratches on the substrate, leading to offset and gain variations of the retrieved signal. ...
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... Many other advanced codes suitable for memory exist in the research literature. Several works have explored source coding and channel coding for fault models other than the BSC by focusing on emerging non-volatile random-access memories (NVMs) [15], [16], [17], [18] and storage-class flash memory [19], [20], [21], [22], [23]. ECCs that are suitable to approximate computing, e.g., Variable-Strength ECC [24] have been proposed. ...
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... The channel is motivated by the properties of flash memory. We give some basic details of this setting here; see [1,9] for more detailed introductions, and see (for example) [6,7,8] for another approach to modelling the problem using rank modulation codes. Flash memory is made up of an array of floating-gate transistors, known as flash cells. ...
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... As a result, the offset between different groups of cells may be very different so that prior art automatic offset or gain control, which estimates the mismatch from the previously received data, can not be applied. Methods to solve these difficulties in Flash memories have been discussed in, for example, [4]- [7]. In optical disc media, such as the popular Compact Disc, DVD, and Blu-ray disc, the retrieved signal depends on the dimensions of the written features and upon the quality of the light path, which may be obscured by fingerprints or scratches on the substrate. ...
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Binary Low Density Parity Check (LDPC) codes have been shown to have near Shannon limit performance when decoded using a probabilistic decoding algorithm. The analogous codes defined over finite fields GF (q) of order q ? 2 show significantly improved performance. We present the results of Monte Carlo simulations of the decoding of infinite LDPC Codes which can be used to obtain good constructions for finite Codes. Our empirical results for the Gaussian channel include a rate 1/4 code with bit error probability of 10 Gamma4 at E b =N 0 = Gamma0:05dB. 1 Introduction We consider a class of error correcting codes first described by Gallager in 1962 [1]. These recently rediscovered low density parity check (LDPC) codes are defined in terms of a sparse parity check matrix and are known to be asymptotically good for all channels with symmetric stationary ergodic noise [2, 3]. Practical decoding of these codes is possible using an approximate belief propagation algorithm and near Shanno...
  • S Lin
  • D J Costello
S. Lin and D. J. Costello, Error Control Coding, 2nd ed. Englewood Cliffs, NJ: Pearson Prentice Hall, 2004.
Introduction to Flash memory
  • R Bez
  • E Camerlanghi
  • A Modelli
  • A Visconti
R. Bez, E. Camerlanghi, A. Modelli, and A. Visconti, "Introduction to Flash memory," Proc. IEEE, vol. 91, no. 4, pp. 489-502, Apr. 2003.