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

TL;DR

This paper analyzes when WOM codes can effectively reduce block erasures in flash memories by introducing the erasure factor metric and comparing two WOM coding schemes, demonstrating that a recent design always improves erasure performance.

Contribution

The paper introduces the erasure factor metric and compares two WOM coding schemes, showing the superiority of a recent design in reducing erasures.

Findings

The erasure factor captures both erasures and data written per block.

The conventional WOM scheme improves erasure factor only up to a storage rate of 0.6442.

The recent WOM scheme always improves the erasure factor regardless of storage rate.

Abstract

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.