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

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

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

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

Generalized Gray Codes for Local Rank Modulation

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.Comment: 7 pages, 1 figure, shorter version was submitted to ISIT 201