Frederic Sala

Dynamic Threshold Schemes for Multi-Level Non-Volatile Memories

In non-volatile memories, reading stored data is typically done through the use of predetermined fixed thresholds. However, due to problems commonly affecting such memories, including voltage drift, overwriting, and inter-cell coupling, fixed threshold usage often results in significant asymmetric errors. To combat these problems, the notion of dynamic thresholds was introduced and applied to the reading of binary sequences. In this paper, we explore the use of dynamic thresholds for multi-level cell (MLC) memories. We provide a general scheme to compute and apply dynamic thresholds and derive performance bounds. We show that the proposed scheme compares favorably with the best-possible thresholding scheme. Finally, we develop asymmetric limited magnitude error-correction codes tailored to take advantage of dynamic thresholds.

Coding for Unreliable Flash Memory Cells

In this work, the model introduced by Gabrys is extended to account for the presence of unreliable memory cells. Leveraging data analysis on errors taking place in a TLC Flash device, we show that memory cells can be broadly categorized into reliable and unreliable cells, where the latter are much more likely to be in error. Our approach programs unreliable cells only in a limited capacity. In particular, we suggest a coding scheme, using generalized tensor product codes, that programs the unreliable cells only at certain voltage levels that are less likely to result in errors. We present simulation results illustrating an improvement of up to a half order of magnitude in page error rates compared to existing codes.

Exact Reconstruction From Insertions in Synchronization Codes

This paper studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and nonbinary sequences from synchronization (insertion/deletion-correcting) codes. These sequences have been corrupted by a fixed number of symbol insertions (larger than the minimum edit distance of the code), yielding a number of distinct traces to be used for reconstruction. We wish to know the minimum number of traces needed for exact reconstruction. This is a general version of a problem tackled by Levenshtein for uncoded sequences. We introduce an exact formula for the maximum number of common supersequences shared by sequences at a certain edit distance, yielding an upper bound on the number of distinct traces necessary to guarantee exact reconstruction. Without specific knowledge of the code words, this upper bound is tight. We apply our results to the famous single deletion/insertion-correcting Varshamov–Tenengolts (VT) codes and show that a significant number of VT code word pairs achieve the worst case number of outputs needed for exact reconstruction. We also consider extensions to other channels, such as adversarial deletion and insertion/deletion channels and probabilistic channels.

Codes Correcting Erasures and Deletions for Rank Modulation

Error-correcting codes for permutations have received considerable attention in the past few years, especially in applications of the rank modulation scheme for flash memories. While codes over several metrics have been studied, such as the Kendall

Analysis and coding schemes for the flash normal-laplace mixture channel

\tau

Three novel combinatorial theorems for the insertion/deletion channel

, Ulam, and Hamming distances, no recent research has been carried out for erasures and deletions over permutations. In rank modulation, flash memory cells represent a permutation, which is induced by their relative charge levels. We explore problems that arise when some of the cells are either erased or deleted. In each case, we study how these erasures and deletions affect the information carried by the remaining cells. In particular, we study models that are symbol-invariant, where unaffected elements do not change their corresponding values from those in the original permutation, or permutation-invariant, where the remaining symbols are modified to form a new permutation with fewer elements. Our main approach in tackling these problems is to build upon the existing works of error-correcting codes and leverage them in order to construct codes in each model of deletions and erasures. The codes we develop are in certain cases asymptotically optimal, while in other cases, such as for codes in the Ulam distance, improve upon the state of the art results.

Error Control Schemes for Modern Flash Memories: Solutions for Flash deficiencies

Error-correcting codes are a critical need for modern flash memories. Such codes are typically designed under the assumption that the voltage threshold distributions in flash cells are Gaussian. This assumption, however, is not realistic. This is particularly the case late in the lifetime of flash devices. A recent work by Parnell et al. provides a parameterized model of MLC (2-bit cell) flash which accurately represents the voltage threshold distributions for an operating period up to 10 times longer than the devices specified lifetime. We analyze this model from an information-theoretic perspective and compute capacity for the resulting channel. We extrapolate the channel from an MLC to a TLC (3-bit cell) model and we characterize the resulting errors. We show that errors under the improved model are highly asymmetric. We introduce a code construction explicitly designed to exploit the asymmetric nature of these errors, and measure its improvement against existing codes at large P/E cycle counts.

Single-deletion-correcting codes over permutations

Although the insertion/deletion problem has been studied for more than fifty years, many results still remain elusive. The goal of this work is to present three novel theorems with a combinatorial flavor that shed further light on the structure and nature of insertions/deletions. In particular, we give an exact result for the maximum number of common supersequences between two sequences, extending older work by Levenshtein. We then generalize this result for sequences that have different lengths. Finally, we compute the exact neighborhood size for the binary circular (alternating) string Cn = 0101 ... 01. In addition to furthering our understanding of the insertion/deletion channel, these theorems can be used as building blocks in other applications. One such application is developing improved lower bounds on the sizes of insertion/deletion-correcting codes.

A practical framework for efficient file synchronization

Flash, already one of the dominant forms of data storage for mobile consumer devices, such as smartphones and media players, is experiencing explosive growth in cloud and enterprise applications. Flash devices offer very high access speeds, low power consumption, and physical resiliency. Our goal in this article is to provide a high-level overview of error correction for Flash. We will begin by discussing Flash functionality and design. We will introduce the nature of Flash deficiencies. Afterwards, we describe the basics of ECCs. We discuss BCH and LDPC codes in particular and wrap up the article with more directions for Flash coding.

NSF expedition on variability-aware software: Recent results and contributions

Motivated by the rank modulation scheme for flash memories, we consider an information representation system with relative values (permutations) and study codes for correcting deletions. In contrast to the case of a deletion in a regular (with absolute values) representation system, a deletion in this new paradigm results in a new permutation over the remaining symbols. For example, the deletion of 3 (or 2) from (1, 3, 2, 4) yields (1, 2, 3); while the deletion of 1 yields (2, 1, 3). Codes for correcting deletions in permutations were studied by Levenshtein under a different model, however, he considered absolute values where the deletions are missing symbols. We study the single deletion relative-values model and prove that a code can correct a single deletion if and only if it can correct a single insertion. Using the concept of a signature of a permutation, we construct single-deletion correcting codes and prove that they are asymptotically optimal with respect to an upper bound that we derive. Finally, we describe an efficient decoding algorithm.