Asymmetric Error Correction and Flash-Memory Rewriting using Polar Codes

We propose efficient coding schemes for two communication settings: 1. asymmetric channels, and 2. channels with an informed encoder. These settings are important in non-volatile memories, as well as optical and broadcast communication. The schemes are based on non-linear polar codes, and they build on and improve recent work on these settings. In asymmetric channels, we tackle the exponential storage requirement of previously known schemes, that resulted from the use of large Boolean functions. We propose an improved scheme, that achieves the capacity of asymmetric channels with polynomial computational complexity and storage requirement. The proposed non-linear scheme is then generalized to the setting of channel coding with an informed encoder, using a multicoding technique. We consider specific instances of the scheme for flash memories, that incorporate error-correction capabilities together with rewriting. Since the considered codes are non-linear, they eliminate the requirement of previously known schemes (called polar write-once-memory codes) for shared randomness between the encoder and the decoder. Finally, we mention that the multicoding scheme is also useful for broadcast communication in Marton's region, improving upon previous schemes for this setting.Comment: Submitted to IEEE Transactions on Information Theory. Partially 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

Algorithms and Data Representations for Emerging Non-Volatile Memories

The evolution of data storage technologies has been extraordinary. Hard disk drives that fit in current personal computers have the capacity that requires tons of transistors to achieve in 1970s. Today, we are at the beginning of the era of non-volatile memory (NVM). NVMs provide excellent performance such as random access, high I/O speed, low power consumption, and so on. The storage density of NVMs keeps increasing following Moore’s law. However, higher storage density also brings significant data reliability issues. When chip geometries scale down, memory cells (e.g. transistors) are aligned much closer to each other, and noise in the devices will become no longer negligible. Consequently, data will be more prone to errors and devices will have much shorter longevity. This dissertation focuses on mitigating the reliability and the endurance issues for two major NVMs, namely, NAND flash memory and phase-change memory (PCM). Our main research tools include a set of coding techniques for the communication channels implied by flash memory and PCM. To approach the problems, at bit level we design error correcting codes tailored for the asymmetric errors in flash and PCM, we propose joint coding scheme for endurance and reliability, error scrubbing methods for controlling storage channel quality, and study codes that are inherently resisting to typical errors in flash and PCM; at higher levels, we are interested in analyzing the structures and the meanings of the stored data, and propose methods that pass such metadata to help further improve the coding performance at bit level. The highlights of this dissertation include the first set of write-once memory code constructions which correct a significant number of errors, a practical framework which corrects errors utilizing the redundancies in texts, the first report of the performance of polar codes for flash memories, and the emulation of rank modulation codes in NAND flash chips

Constructions of Rank Modulation Codes

Rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines. Modeling rank modulation involves construction of packings of the space of permutations equipped with the Kendall tau distance. We present several general constructions of codes in permutations that cover a broad range of code parameters. In particular, we show a number of ways in which conventional error-correcting codes can be modified to correct errors in the Kendall space. Codes that we construct afford simple encoding and decoding algorithms of essentially the same complexity as required to correct errors in the Hamming metric. For instance, from binary BCH codes we obtain codes correcting $t$ Kendall errors in $n$ memory cells that support the order of $n!/(\log_2n!)^t$ messages, for any constant $t= 1,2,...$ We also construct families of codes that correct a number of errors that grows with $n$ at varying rates, from $\Theta(n)$ to $\Theta(n^{2})$. One of our constructions gives rise to a family of rank modulation codes for which the trade-off between the number of messages and the number of correctable Kendall errors approaches the optimal scaling rate. Finally, we list a number of possibilities for constructing codes of finite length, and give examples of rank modulation codes with specific parameters.Comment: Submitted to IEEE Transactions on Information Theor

Rank-Modulation Rewrite Coding for Flash Memories

The current flash memory technology focuses on the cost minimization of its static storage capacity. However, the resulting approach supports a relatively small number of program-erase cycles. This technology is effective for consumer devices (e.g., smartphones and cameras) where the number of program-erase cycles is small. However, it is not economical for enterprise storage systems that require a large number of lifetime writes. The proposed approach in this paper for alleviating this problem consists of the efficient integration of two key ideas: 1) improving reliability and endurance by representing the information using relative values via the rank modulation scheme and 2) increasing the overall (lifetime) capacity of the flash device via rewriting codes, namely, performing multiple writes per cell before erasure. This paper presents a new coding scheme that combines rank-modulation with rewriting. The key benefits of the new scheme include: 1) the ability to store close to 2 bit per cell on each write with minimal impact on the lifetime of the memory and 2) efficient encoding and decoding algorithms that make use of capacity-achieving write-once-memory codes that were proposed recently

Lossy Compression with Privacy Constraints: Optimality of Polar Codes

A lossy source coding problem with privacy constraint is studied in which two correlated discrete sources $X$ and $Y$ are compressed into a reconstruction $\hat{X}$ with some prescribed distortion $D$. In addition, a privacy constraint is specified as the equivocation between the lossy reconstruction $\hat{X}$ and $Y$. This models the situation where a certain amount of source information from one user is provided as utility (given by the fidelity of its reconstruction) to another user or the public, while some other correlated part of the source information $Y$ must be kept private. In this work, we show that polar codes are able, possibly with the aid of time sharing, to achieve any point in the optimal rate-distortion-equivocation region identified by Yamamoto, thus providing a constructive scheme that obtains the optimal tradeoff between utility and privacy in this framework.Comment: Submitted for publicatio

Error correction and partial information rewriting for flash memories

This paper considers the partial information rewriting problem for flash memories. In this problem, the state of information can only be updated to a limited number of new states, and errors may occur in memory cells between two adjacent updates. We propose two coding schemes based on the models of trajectory codes. The bounds on achievable code rates are shown using polar WOM coding. Our schemes generalize the existing rewriting codes in multiple ways, and can be applied to various practical scenarios such as file editing, log-based file systems and file synchronization systems

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