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ABSTRACT: We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rank-modulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study Gray codes for the local rank-modulation scheme in order to simulate conventional multi-level flash cells while retaining the benefits of rank modulation. Unlike the limited scope of previous works, we consider code constructions for the entire range of parameters including the code length, sliding window size, and overlap between adjacent windows. We show our constructed codes have asymptotically-optimal rate. We also provide efficient encoding, decoding, and next-state algorithms.
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on; 09/2011
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ABSTRACT: Rank modulation has been recently proposed as a scheme for storing information in flash memories. While rank modulation has advantages in improving write speed and endurance, the current encoding approach is based on the “push to the top” operation that is not efficient in the general case. We propose a new encoding procedure where a cell level is raised to be higher than the minimal necessary subset -instead of all - of the other cell levels. This new procedure leads to a significantly more compressed (lower charge levels) encoding. We derive an upper bound for a family of codes that utilize the proposed encoding procedure, and consider code constructions that achieve that bound for several special cases.
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on; 09/2011
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ABSTRACT: For many nonvolatile memories, - including flash memories, phase-change memories, etc., - maximizing the storage capacity is a key challenge. The existing method is to use multilevel cells (MLC) of more and more levels. The number of levels supported by MLC is seriously constrained by the worst-case performance of cell-programming noise and cell heterogeneity. In this paper, we present variable-level cells (VLC), a new scheme for maximum storage capacity. It adaptively chooses the number of levels and the placement of the levels based on the actual programming performance. We derive its storage capacity, and present an optimal data representation scheme. We also study rewriting schemes for VLC, and present inner and outer bounds to its capacity region.
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on; 09/2011
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ABSTRACT: Phase-change memory (PCM) is an emerging nonvolatile memory technology that promises very high performance. It currently uses discrete cell levels to represent data, controlled by a single amorphous/crystalline domain in a cell. To improve data density, more levels per cell are needed. There exist a number of challenges, including cell programming noise, drifting of cell levels, and the high power requirement for cell programming. In this paper, we present a new cell structure called patterned cell, and explore its data representation schemes. Multiple domains per cell are used, and their connectivity is used to store data. We analyze its storage capacity, and study its error-correction capability and the construction of error-control codes.
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on; 09/2011
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ABSTRACT: Predetermined fixed thresholds are commonly used in nonvolatile memories for reading binary sequences, but they usually result in significant asymmetric errors after a long duration, due to voltage or resistance drift. This motivates us to construct error-correcting schemes with dynamic reading thresholds, so that the asymmetric component of errors are minimized. In this paper, we discuss how to select dynamic reading thresholds without knowing cell level distributions, and present several error-correcting schemes. Analysis based on Gaussian noise models reveals that bit error probabilities can be significantly reduced by using dynamic thresholds instead of fixed thresholds, hence leading to a higher information rate.
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on; 09/2011
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ABSTRACT: We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. The local rank-modulation, as a generalization of the rank-modulation scheme, has been recently suggested as a way of storing information in flash memory. We study constant-weight Gray codes for the local rank-modulation scheme in order to simulate conventional multilevel flash cells while retaining the benefits of rank modulation. We describe a construction for a codes of rate tending to 1.
Electrical and Electronics Engineers in Israel (IEEEI), 2010 IEEE 26th Convention of; 12/2010
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ABSTRACT: Memories whose storage cells transit irreversibly between states have been common since the start of the data storage technology. In recent years, flash memories have become a very important family of such memories. A flash memory cell has q states-state 0, 1, ..., q-1-and can only transit from a lower state to a higher state before the expensive erasure operation takes place. We study rewriting codes that enable the data stored in a group of cells to be rewritten by only shifting the cells to higher states. Since the considered state transitions are irreversible, the number of rewrites is bounded. Our objective is to maximize the number of times the data can be rewritten. We focus on the joint storage of data in flash memories, and study two rewriting codes for two different scenarios. The first code, called floating code, is for the joint storage of multiple variables, where every rewrite changes one variable. The second code, called buffer code, is for remembering the most recent data in a data stream. Many of the codes presented here are either optimal or asymptotically optimal. We also present bounds to the performance of general codes. The results show that rewriting codes can integrate a flash memory's rewriting capabilities for different variables to a high degree.
IEEE Transactions on Information Theory 11/2010; · 3.01 Impact Factor
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ABSTRACT: Phase-change memories (PCMs) are an important emerging non-volatile memory technology that uses amorphous and crystalline cell states to store data. The cell states are switched using high temperatures. As the semi-stable states of PCM cells are sensitive to temperatures, scaling down cell sizes can bring significant challenges. We consider two potential thermal-based interference problems as the cell density approaches its limit, and study new constrained codes for them.
Information Theory Workshop (ITW), 2010 IEEE; 10/2010
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ABSTRACT: We investigate error-correcting codes for a the rank-modulation scheme with an application to flash memory devices. In this scheme, a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The resulting scheme eliminates the need for discrete cell levels, overcomes overshoot errors when programming cells (a serious problem that reduces the writing speed), and mitigates the problem of asymmetric errors. In this paper, we study the properties of error-correcting codes for charge-constrained errors in the rank-modulation scheme. In this error model the number of errors corresponds to the minimal number of adjacent transpositions required to change a given stored permutation to another erroneous one-a distance measure known as Kendall's ¿ -distance. We show bounds on the size of such codes, and use metric-embedding techniques to give constructions which translate a wealth of knowledge of codes in the Lee metric to codes over permutations in Kendall's ¿ -metric. Specifically, the one-error-correcting codes we construct are at least half the ball-packing upper bound.
IEEE Transactions on Information Theory 06/2010; · 3.01 Impact Factor
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ABSTRACT: NAND flash memories are the most widely used non-volatile memories, and data movement is common in flash storage systems. We study data movement solutions that minimize the number of block erasures, which are very important for the efficiency and longevity of flash memories. To move data among n blocks with the help of ¿ auxiliary blocks, where every block contains m pages, we present algorithms that use ¿(n · min{m, log<sub>¿</sub> n}) erasures without the tool of coding. We prove this is almost the best possible for non-coding solutions by presenting a nearly matching lower bound. Optimal data movement can be achieved using coding, where only ¿(n) erasures are needed. We present a coding-based algorithm, which has very low coding complexity, for optimal data movement. We further show the NP hardness of both coding-based and non-coding schemes when the objective is to optimize data movement on a per instance basis.
Communication, Control, and Computing, 2009. Allerton 2009. 47th Annual Allerton Conference on; 11/2009
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ABSTRACT: Flash memories are a very widely used type of non-volatile memory. Like magnetic recording and optical recording, flash memories have their own distinct properties. These distinct properties introduce very interesting information-representation and coding problems, which address many aspects of a successful storage system. In this paper, we survey recent results in this area. A focus is placed on rewriting codes and rank modulation.
Communications, Computers and Signal Processing, 2009. PacRim 2009. IEEE Pacific Rim Conference on; 09/2009
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ABSTRACT: A constrained memory is a storage device whose elements change their states under some constraints. A typical example is flash memories, in which cell levels are easy to increase but hard to decrease. In a general rewriting model, the stored data changes with some pattern determined by the application. In a constrained memory, an appropriate representation is needed for the stored data to enable efficient rewriting. In this paper, we define the general rewriting problem using a graph model. This model generalizes many known rewriting models such as floating codes, WOM codes, buffer codes, etc. We present a novel rewriting scheme for the flash-memory model and prove it is asymptotically optimal in a wide range of scenarios. We further study randomization and probability distributions to data rewriting and study the expected performance. We present a randomized code for all rewriting sequences and a deterministic code for rewriting following any i.i.d. distribution. Both codes are shown to be optimal asymptotically.
Information Theory, 2009. ISIT 2009. IEEE International Symposium on; 08/2009
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ABSTRACT: We explore a novel data representation scheme for multilevel flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The only allowed charge-placement mechanism is a ldquopush-to-the-toprdquo operation, which takes a single cell of the set and makes it the top-charged cell. The resulting scheme eliminates the need for discrete cell levels, as well as overshoot errors, when programming cells. We present unrestricted Gray codes spanning all possible n-cell states and using only "push-to-the-top" operations, and also construct balanced Gray codes. One important application of the Gray codes is the realization of logic multilevel cells, which is useful in conventional storage solutions. We also investigate rewriting schemes for random data modification. We present both an optimal scheme for the worst case rewrite performance and an approximation scheme for the average-case rewrite performance.
IEEE Transactions on Information Theory 07/2009; · 3.01 Impact Factor
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ABSTRACT: The existence of a perfect 1-factorization of the complete graph with n nodes, namely, K<sub>n</sub> , for arbitrary even number n, is a 40-year-old open problem in graph theory. So far, two infinite families of perfect 1-factorizations have been shown to exist, namely, the factorizations of <sub>Kp+1</sub> and K<sub>2</sub> <sub>p</sub> , where p is an arbitrary prime number (p > 2) . It was shown in previous work that finding a perfect 1 -factorization of K<sub>n</sub> is related to a problem in coding, specifically, it can be reduced to constructing an MDS (Minimum Distance Separable), lowest density array code. In this paper, a new method for shortening arbitrary array codes is introduced. It is then used to derive the K<sub>p+1</sub> family of perfect 1 -factorization from the K<sub>2p</sub> family. Namely, techniques from coding theory are used to prove a new result in graph theory-that the two factorization families are related.
IEEE Transactions on Information Theory 03/2009; · 3.01 Impact Factor
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ABSTRACT: In this work, we study the computational perspective of network coding, focusing on two issues. First, we address the computational complexity of finding a network code for acyclic multicast networks. Second, we address the issue of reducing the amount of computation performed by network nodes. In particular, we consider the problem of finding a network code with the minimum possible number of encoding nodes, i.e. nodes that generate new packets by performing algebraic operations on packets received over incoming links.We present a deterministic algorithm that finds a feasible network code for a multicast network over an underlying graph G(V,E) in time 0(Ekh + Vk<sup>2</sup>h<sup>2</sup> + h<sup>4</sup>k<sup>3</sup>(k + h)), where k is the number of destinations and h is the number of packets. Our algorithm improves the best known running time for network code construction. In addition, our algorithm guarantees that the number of encoding nodes in the obtained network code is upper- bounded by 0(h<sup>3</sup>k<sup>2</sup>). Next, we address the problem of finding integral and fractional network codes with the minimum number of encoding nodes. We prove that in the majority of settings this problem is NP-hard. However, we show that if h = O(1),k = O(1), and the underlying communication graph is acyclic, then there exists an algorithm that solves this problem in polynomial time.
IEEE Transactions on Information Theory 02/2009; · 3.01 Impact Factor
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ABSTRACT: Flash memories are the most widely used type of non-volatile electronic memories. Compared to magnetic recording and optical recording, flash memories have the unique property that their cell levels, which represent data, are programmed using an iterative procedure that monotonically shifts each cell level upward toward its target value. In this paper, we study the capacity of flash memories to store data. We explore the relationship among their capacity, programming precision and programming time. The study is focused on the capacity of single cells, and an optimal programming algorithm is presented.
Information Theory and Its Applications, 2008. ISITA 2008. International Symposium on; 01/2009
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ABSTRACT: We study broadcast systems that distribute a series of data updates to a large number of passive clients. The updates are sent over a broadcast channel in the form of discrete packets. We assume that clients periodically access the channel to obtain the most recent update. Such scenarios arise in many practical applications, such as distribution of traffic information and market updates to mobile wireless devices. Our goal is to design broadcast schedules that minimize the waiting time, i.e., the amount of time the client needs to wait in order to obtain the most recent update. We assume that each client has a different access pattern depending on the channel conditions, computing power, and storage capabilities. We introduce and analyze optimal universal schedules that guarantee low waiting time for any client, regardless of its behavior.
IEEE Transactions on Information Theory 10/2008; · 3.01 Impact Factor
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ABSTRACT: Flash memory is an electronic non-volatile memory with wide applications. Due to the substantial impact of block erasure operations on the speed, reliability and longevity of flash memories, writing schemes that enable data to be modified numerous times without incurring the block erasure is desirable. This requirement is addressed by floating codes, a coding scheme that jointly stores and rewrites data and maximizes the rewriting capability of flash memories. In this paper, we present several new floating code constructions. They include both codes with specific parameters and general code constructions that are asymptotically optimal. We also present bounds to the performance of floating codes.
Information Theory, 2008. ISIT 2008. IEEE International Symposium on; 08/2008
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ABSTRACT: We investigate error-correcting codes for a novel storage technology for flash memories, the rank-modulation scheme. In this scheme, a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The resulting scheme eliminates the need for discrete cell levels, overcomes overshoot errors when programming cells (a serious problem that reduces the writing speed), and mitigates the problem of asymmetric errors. In this paper, we study the properties of error correction in rank modulation codes. We show that the adjacency graph of permutations is a subgraph of a multi-dimensional array of a special size, a property that enables code designs based on Lee- metric codes. We present a one-error-correcting code whose size is at least half of the optimal size. We also present additional error-correcting codes and some related bounds.
Information Theory, 2008. ISIT 2008. IEEE International Symposium on; 08/2008
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ABSTRACT: Randomness is inherent to biochemistry: at each instant, the sequence of reactions that fires is a matter of chance. Some biological systems exploit such randomness, choosing between different outcomes stochastically - in effect, hedging their bets with a portfolio of responses for different environmental conditions. In this paper, we discuss techniques for synthesizing such stochastic behavior in engineered biochemical systems. We propose a general method for designing a set of biochemical reactions that produces different combinations of molecular types according to a specified probability distribution. The response is precise and robust to perturbations. Furthermore, it is programmable: the probability distribution is a function of the quantities of input types. The method is modular and extensible. We discuss strategies for implementing various functional dependencies: linear, logarithmic, exponential, etc. This work has potential applications in domains such as biochemical sensing, drug production, and disease treatment. Moreover, it provides a framework for analyzing and characterizing the stochastic dynamics in natural biochemical systems such as the lysis/lysogeny switch of the lambda bacteriophage.
Design Automation Conference, 2007. DAC '07. 44th ACM/IEEE; 07/2007
