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

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

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

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

저밀도 부호의 응용: 묶음 지그재그 파운틴 부호와 WOM 부호

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 노종선.This dissertation contains the following two contributions on the applications of sparse codes. Fountain codes Batched zigzag (BZ) fountain codes – Two-phase batched zigzag (TBZ) fountain codes Write-once memory (WOM) codes – WOM codes implemented by rate-compatible low-density generator matrix (RC-LDGM) codes First, two classes of fountain codes, called batched zigzag fountain codes and two-phase batched zigzag fountain codes, are proposed for the symbol erasure channel. At a cost of slightly lengthened code symbols, the involved message symbols in each batch of the proposed codes can be recovered by low complexity zigzag decoding algorithm. Thus, the proposed codes have low buffer occupancy during decoding process. These features are suitable for receivers with limited hardware resources in the broadcasting channel. A method to obtain degree distributions of code symbols for the proposed codes via ripple size evolution is also proposed by taking into account the released code symbols from the batches. It is shown that the proposed codes outperform Luby transform codes and zigzag decodable fountain codes with respect to intermediate recovery rate and coding overhead when message length is short, symbol erasure rate is low, and available buffer size is limited. In the second part of this dissertation, WOM codes constructed by sparse codes are presented. Recently, WOM codes are adopted to NAND flash-based solid-state drive (SSD) in order to extend the lifetime by reducing the number of erasure operations. Here, a new rewriting scheme for the SSD is proposed, which is implemented by multiple binary erasure quantization (BEQ) codes. The corresponding BEQ codes are constructed by RC-LDGM codes. Moreover, by putting RC-LDGM codes together with a page selection method, writing efficiency can be improved. It is verified via simulation that the SSD with proposed rewriting scheme outperforms the SSD without and with the conventional WOM codes for single level cell (SLC) and multi-level cell (MLC) flash memories.1 Introduction 1 1.1 Background 1 1.2 Overview of Dissertation 5 2 Sparse Codes 7 2.1 Linear Block Codes 7 2.2 LDPC Codes 9 2.3 Message Passing Decoder 11 3 New Fountain Codes with Improved Intermediate Recovery Based on Batched Zigzag Coding 13 3.1 Preliminaries 17 3.1.1 Definitions and Notation 17 3.1.2 LT Codes 18 3.1.3 Zigzag Decodable Codes 20 3.1.4 Bit-Level Overhead 22 3.2 New Fountain Codes Based on Batched Zigzag Coding 23 3.2.1 Construction of Shift Matrix 24 3.2.2 Encoding and Decoding of the Proposed BZ Fountain Codes 25 3.2.3 Storage and Computational Complexity 28 3.3 Degree Distribution of BZ Fountain Codes 31 3.3.1 Relation Between $\Psi(x)$ and $\Omega(x)$ 31 3.3.2 Derivation of $\Omega(x)$ via Ripple Size Evolution 32 3.4 Two-Phase Batched Zigzag Fountain Codes with Additional Memory 40 3.4.1 Code Construction 41 3.4.2 Bit-Level Overhead 46 3.5 Numerical Analysis 49 4 Write-Once Memory Codes Using Rate-Compatible LDGM Codes 60 4.1 Preliminaries 62 4.1.1 NAND Flash Memory 62 4.1.2 Rewriting Schemes for Flash Memory 62 4.1.3 Construction of Rewriting Codes by BEQ Codes 65 4.2 Proposed Rewriting Codes 67 4.2.1 System Model 67 4.2.2 Multi-rate Rewriting Codes 68 4.2.3 Page Selection for Rewriting 70 4.3 RC-LDGM Codes 74 4.4 Numerical Analysis 76 5 Conclusions 80 Bibliography 82 초록 94Docto

Signal Processing for Caching Networks and Non-volatile Memories

The recent information explosion has created a pressing need for faster and more reliable data storage and transmission schemes. This thesis focuses on two systems: caching networks and non-volatile storage systems. It proposes network protocols to improve the efficiency of information delivery and signal processing schemes to reduce errors at the physical layer as well. This thesis first investigates caching and delivery strategies for content delivery networks. Caching has been investigated as a useful technique to reduce the network burden by prefetching some contents during o˙-peak hours. Coded caching [1] proposed by Maddah-Ali and Niesen is the foundation of our algorithms and it has been shown to be a useful technique which can reduce peak traffic rates by encoding transmissions so that different users can extract different information from the same packet. Content delivery networks store information distributed across multiple servers, so as to balance the load and avoid unrecoverable losses in case of node or disk failures. On one hand, distributed storage limits the capability of combining content from different servers into a single message, causing performance losses in coded caching schemes. But, on the other hand, the inherent redundancy existing in distributed storage systems can be used to improve the performance of those schemes through parallelism. This thesis proposes a scheme combining distributed storage of the content in multiple servers and an efficient coded caching algorithm for delivery to the users. This scheme is shown to reduce the peak transmission rate below that of state-of-the-art algorithms

Towards Endurable, Reliable and Secure Flash Memories-a Coding Theory Application

Storage systems are experiencing a historical paradigm shift from hard disk to nonvolatile memories due to its advantages such as higher density, smaller size and non-volatility. On the other hand, Solid Storage Disk (SSD) also poses critical challenges to application and system designers. The first challenge is called endurance. Endurance means flash memory can only experience a limited number of program/erase cycles, and after that the cell quality degradation can no longer be accommodated by the memory system fault tolerance capacity. The second challenge is called reliability, which means flash cells are sensitive to various noise and disturbs, i.e., data may change unintentionally after experiencing noise/disturbs. The third challenge is called security, which means it is impossible or costly to delete files from flash memory securely without leaking information to possible eavesdroppers. In this dissertation, we first study noise modeling and capacity analysis for NAND flash memories (which is the most popular flash memory in market), which gains us some insight on how flash memories are working and their unique noise. Second, based on the characteristics of content-replication codewords in flash memories, we propose a joint decoder to enhance the flash memory reliability. Third, we explore data representation schemes in flash memories and optimal rewriting code constructions in order to solve the endurance problem. Fourth, in order to make our rewriting code more practical, we study noisy write-efficient memories and Write-Once Memory (WOM) codes against inter-cell interference in NAND memories. Finally, motivated by the secure deletion problem in flash memories, we study coding schemes to solve both the endurance and the security issues in flash memories. This work presents a series of information theory and coding theory research studies on the aforesaid three critical issues, and shows that how coding theory can be utilized to address these challenges