Rewriting Codes for Joint Information Storage in Flash Memories

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

Trajectory Codes for Flash Memory

Flash memory is well-known for its inherent asymmetry: the flash-cell charge levels are easy to increase but are hard to decrease. In a general rewriting model, the stored data changes its value with certain patterns. The patterns of data updates are determined by the data structure and the application, and are independent of the constraints imposed by the storage medium. Thus, an appropriate coding scheme is needed so that the data changes can be updated and stored efficiently under the storage-medium's constraints. In this paper, we define the general rewriting problem using a graph model. It extends many known rewriting models such as floating codes, WOM codes, buffer codes, etc. We present a new rewriting scheme for flash memories, called the trajectory code, for rewriting the stored data as many times as possible without block erasures. We prove that the trajectory code is asymptotically optimal in a wide range of scenarios. We also present randomized rewriting codes optimized for expected performance (given arbitrary rewriting sequences). Our rewriting codes are shown to be asymptotically optimal.Comment: Submitted to IEEE Trans. on Inform. Theor

Unfolding-based Partial Order Reduction

Partial order reduction (POR) and net unfoldings are two alternative methods to tackle state-space explosion caused by concurrency. In this paper, we propose the combination of both approaches in an effort to combine their strengths. We first define, for an abstract execution model, unfolding semantics parameterized over an arbitrary independence relation. Based on it, our main contribution is a novel stateless POR algorithm that explores at most one execution per Mazurkiewicz trace, and in general, can explore exponentially fewer, thus achieving a form of super-optimality. Furthermore, our unfolding-based POR copes with non-terminating executions and incorporates state-caching. Over benchmarks with busy-waits, among others, our experiments show a dramatic reduction in the number of executions when compared to a state-of-the-art DPOR.Comment: Long version of a paper with the same title appeared on the proceedings of CONCUR 201

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

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

The Capacity of Write-Once Memory with a Writing Cost Function

書換に制限を有する記憶媒体というのは古今東西存在する．例えば，パンチカードは一度穴を開けたら塞ぐことができない．またフラッシュメモリにおいては，ブロック消去と呼ばれる特別な操作を行わなければ，記憶素子であるセル内部の電荷を減らすことができない．R.L. RivestとA. Shamirは1982年に，そのような制限を有する記憶媒体のモデルとしてWrite-Once Memory (WOM)を導入した．そして彼らは，WOMを複数回にわたり書換える際，書込可能なメッセージの量をなるべく多くするための工夫とはどのようなものかを提示した．そのような工夫は，WOM符号化と呼ばれている．オリジナルのWOMでは記憶素子の取りうる状態が二値であったが，その後1984年にA. FiatとA. Shamirにより，多値を扱える一般化WOMが提案された．一般化WOMでは，素子の取りうる状態および状態間の可能な遷移を，無閉路有向グラフによって指定する．WOMにおいて興味深い問題の一つは，最良の符号化によりどれだけ多くのメッセージを書込めるかということである．この問題に対する解答として，F. FuとA.J. Han Vinckは1999年に，任意の一般化WOMにおける容量域と最大和率を決定した．本研究では，一般化WOMをさらに拡張したWrite-Constrained Memory (WCM)を提案する．WCMの大きな特徴の一つは，それが状態遷移のコストを考慮することである．実用的には，状態遷移コストは時間やエネルギーといった物理量としての意味を持つものであり，何らかの理由でそれを制限しなければならないという状況が想定される．本研究ではそのような制限の一つとして，WCMに対する平均コスト制約というものを提案する．本研究における主要な結果は，任意のWCMにおいて，定数回にわたり書換える際，平均コスト制約を満足する容量域および最大和率を決定したことである．電気通信大学201

Minimizing Running Costs in Consumption Systems

A standard approach to optimizing long-run running costs of discrete systems is based on minimizing the mean-payoff, i.e., the long-run average amount of resources ("energy") consumed per transition. However, this approach inherently assumes that the energy source has an unbounded capacity, which is not always realistic. For example, an autonomous robotic device has a battery of finite capacity that has to be recharged periodically, and the total amount of energy consumed between two successive charging cycles is bounded by the capacity. Hence, a controller minimizing the mean-payoff must obey this restriction. In this paper we study the controller synthesis problem for consumption systems with a finite battery capacity, where the task of the controller is to minimize the mean-payoff while preserving the functionality of the system encoded by a given linear-time property. We show that an optimal controller always exists, and it may either need only finite memory or require infinite memory (it is decidable in polynomial time which of the two cases holds). Further, we show how to compute an effective description of an optimal controller in polynomial time. Finally, we consider the limit values achievable by larger and larger battery capacity, show that these values are computable in polynomial time, and we also analyze the corresponding rate of convergence. To the best of our knowledge, these are the first results about optimizing the long-run running costs in systems with bounded energy stores.Comment: 32 pages, corrections of typos and minor omission