Trade-offs between Instantaneous and Total Capacity in Multi-Cell Flash Memories

The limited endurance of flash memories is a major design concern for enterprise storage systems. We propose a method to increase it by using relative (as opposed to fixed) cell levels and by representing the information with Write Asymmetric Memory (WAM) codes. Overall, our new method enables faster writes, improved reliability as well as improved endurance by allowing multiple writes between block erasures. We study the capacity of the new WAM codes with relative levels, where the information is represented by multiset permutations induced by the charge levels, and show that it achieves the capacity of any other WAM codes with the same number of writes. Specifically, we prove that it has the potential to double the total capacity of the memory. Since capacity can be achieved only with cells that have a large number of levels, we propose a new architecture that consists of multi-cells - each an aggregation of a number of floating gate transistors

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

On Coding Efficiency for Flash Memories

Recently, flash memories have become a competitive solution for mass storage. The flash memories have rather different properties compared with the rotary hard drives. That is, the writing of flash memories is constrained, and flash memories can endure only limited numbers of erases. Therefore, the design goals for the flash memory systems are quite different from these for other memory systems. In this paper, we consider the problem of coding efficiency. We define the "coding-efficiency" as the amount of information that one flash memory cell can be used to record per cost. Because each flash memory cell can endure a roughly fixed number of erases, the cost of data recording can be well-defined. We define "payload" as the amount of information that one flash memory cell can represent at a particular moment. By using information-theoretic arguments, we prove a coding theorem for achievable coding rates. We prove an upper and lower bound for coding efficiency. We show in this paper that there exists a fundamental trade-off between "payload" and "coding efficiency". The results in this paper may provide useful insights on the design of future flash memory systems.Comment: accepted for publication in the Proceeding of the 35th IEEE Sarnoff Symposium, Newark, New Jersey, May 21-22, 201

New constructions of WOM codes using the Wozencraft ensemble

In this paper we give several new constructions of WOM codes. The novelty in our constructions is the use of the so called Wozencraft ensemble of linear codes. Specifically, we obtain the following results. We give an explicit construction of a two-write Write-Once-Memory (WOM for short) code that approaches capacity, over the binary alphabet. More formally, for every \epsilon>0, 0<p<1 and n =(1/\epsilon)^{O(1/p\epsilon)} we give a construction of a two-write WOM code of length n and capacity H(p)+1-p-\epsilon. Since the capacity of a two-write WOM code is max_p (H(p)+1-p), we get a code that is \epsilon-close to capacity. Furthermore, encoding and decoding can be done in time O(n^2.poly(log n)) and time O(n.poly(log n)), respectively, and in logarithmic space. We obtain a new encoding scheme for 3-write WOM codes over the binary alphabet. Our scheme achieves rate 1.809-\epsilon, when the block length is exp(1/\epsilon). This gives a better rate than what could be achieved using previous techniques. We highlight a connection to linear seeded extractors for bit-fixing sources. In particular we show that obtaining such an extractor with seed length O(log n) can lead to improved parameters for 2-write WOM codes. We then give an application of existing constructions of extractors to the problem of designing encoding schemes for memory with defects.Comment: 19 page