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

Correcting Charge-Constrained Errors in the Rank-Modulation Scheme

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 τ-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 τ-metric. Specifically, the one-error-correcting codes we construct are at least half the ball-packing upper bound

"Ein Wahnsinniger, der die Fakultäten vermischt" : interdisciplinarity and Ingeborg Bachmann's Das Buch Franza

This paper seeks to demonstrate the ways in which Bachmann's work constitutes a prime case for examining the scope and the boundaries of philological research. It does so by focusing on Bachmann‘s fragmentary and unfinished novel, "Das Buch Franza" [1965-1966], exploring the text and its author in an interdisciplinary light. Forming part of Bachmann's uncompleted "Todesarten"-Projekt, "Das Buch Franza" deals with the continuing legacy of fascism and its displaced forms in the post-war era. In its thematisation of the traumatic and necessarily belated after-effects of the Second World War and the Holocaust, Bachmann‘s text draws on various disciplines and discourses, namely geology, archaeology and psychoanalysis. I consider the ways in which the interdisciplinary ambitions of the text reflect Bachmann‘s struggle for a new form of representation, one that adequately mirrors the concerns of her society. Finally, drawing on Bachmann‘s own theoretical reflections on the field of literary study in her Frankfurt Lectures on poetics, I trace the ways in which the author's work repeatedly encourages us to adopt multiple disciplinary perspectives, as well as privileging literature with a utopian function that exceeds any generic or disciplinary boundaries

An empirical investigation of sparse distributed memory using discrete speech recognition

Presented here is a step by step analysis of how the basic Sparse Distributed Memory (SDM) model can be modified to enhance its generalization capabilities for classification tasks. Data is taken from speech generated by a single talker. Experiments are used to investigate the theory of associative memories and the question of generalization from specific instances

Self-Learning Hot Data Prediction: Where Echo State Network Meets NAND Flash Memories

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Well understanding the access behavior of hot data is significant for NAND flash memory due to its crucial impact on the efficiency of garbage collection (GC) and wear leveling (WL), which respectively dominate the performance and life span of SSD. Generally, both GC and WL rely greatly on the recognition accuracy of hot data identification (HDI). However, in this paper, the first time we propose a novel concept of hot data prediction (HDP), where the conventional HDI becomes unnecessary. First, we develop a hybrid optimized echo state network (HOESN), where sufficiently unbiased and continuously shrunk output weights are learnt by a sparse regression based on L2 and L1/2 regularization. Second, quantum-behaved particle swarm optimization (QPSO) is employed to compute reservoir parameters (i.e., global scaling factor, reservoir size, scaling coefficient and sparsity degree) for further improving prediction accuracy and reliability. Third, in the test on a chaotic benchmark (Rossler), the HOESN performs better than those of six recent state-of-the-art methods. Finally, simulation results about six typical metrics tested on five real disk workloads and on-chip experiment outcomes verified from an actual SSD prototype indicate that our HOESN-based HDP can reliably promote the access performance and endurance of NAND flash memories.Peer reviewe

Guido Weiss: a few memories of a friend and an influential mathematician

This contribution starts with an exchange between us on the way we met Guido and he influenced our mathematical lives. Then it is mainly a survey paper that illustrates this influence by describing different topics and their subsequent evolution after his seminal papers and courses. Our main thread is the notion of a space of homogeneous type. In the second section we describe how it became central in pluricomplex analysis and consider particularly the existence of weak factorization for spaces of holomorphic functions. In the last section, one revisits the construction of a basis of wavelets in a space of homogeneous type and the way it allows a Littlewood-Paley analysis