Storage coding for wear leveling in flash memories

Abstract

Abstract-Flash memory is a nonvolatile computer memory comprised of blocks of cells, wherein each cell is implemented as either NAND or NOR floating gate. NAND flash is currently the most widely used type of flash memory. In a NAND flash memory, every block of cells consists of numerous pages; rewriting even a single page requires the whole block to be erased and reprogrammed. Block erasures determine both the longevity and the efficiency of a flash memory. Therefore, when data in a NAND flash memory are reorganized, minimizing the total number of block erasures required to achieve the desired data movement is an important goal. This leads to the flash data movement problem studied in this paper. We show that coding can significantly reduce the number of block erasures required for data movement, and present several optimal or nearly optimal data-movement algorithms based upon ideas from coding theory and combinatorics. In particular, we show that the sorting-based (noncoding) schemes require O(n log n) erasures to move data among n blocks, whereas coding-based schemes require only O(n) erasures. Furthermore, coding-based schemes use only one auxiliary block, which is the best possible and achieve a good balance between the number of erasures in each of the n + 1 blocks.

Data Representation for Flash Memories

“…The block erasure property of flash memories affects not only rewriting and cell programming, but also data movement. In [22], it is shown that by appropriately using coding, the number of erasures needed for moving data among n NAND flash blocks can be reduced by a factor of O(log n). The rewriting codes and the rank modulation scheme are useful not only for flash memories, but also for other constrained memories.…”

Data movement and aggregation in flash memories

“…Therefore, it is critical to minimize the number of erasures when data are reorganized [2]. This leads to the data movement problem, which has been studied in [3], [5]. Although data movement is common in all storage systems, the unique block erasure property of flash memories calls for special solutions.…”

“…In the data movement problem [3], [5], there are n blocks storing data, where every block has m pages. The nm pages of data need to be switched among the n blocks with specified destinations.…”

“…The objective is to minimize the number of block erasures. It was proved in [5] that optimal solutions can be obtained by using coding. Furthermore, a coding-based algorithm using at most 2n − 1 erasures for δ = 1 was presented [5], which is worst-case optimal.…”

“…It was proved in [5] that optimal solutions can be obtained by using coding. Furthermore, a coding-based algorithm using at most 2n − 1 erasures for δ = 1 was presented [5], which is worst-case optimal. The algorithm in [5] requires coding over a large Galois field; to reduce the coding complexity, it was shown in [3] later that there exist solutions with coding over GF(q) for q ≥ 3.…”