NAND \ufb02ash memories have become the most widely used type of non-volatile memories. In a NAND \ufb02ash memory, every block of memory cells consists of numerous pages, and rewriting a single page requires the whole block to be erased. As block erasures signi\ufb01cantly reduce the longevity, speed and power ef\ufb01ciency of \ufb02ash memories, it is critical to minimize the number of erasures when data are reorganized. This leads to the data movement problem, where data need to be switched in blocks, and the objective is to minimize the number of block erasures. It has been shown that optimal solutions can be obtained by coding. However, coding-based algorithms with the minimum coding complexity still remain an important topic to study. In this paper, we present a very ef\ufb01cient data movement algorithm with coding over GF(2) and with the minimum storage requirement. We also study data movement with more auxiliary blocks and present its corresponding solution. Furthermore, we extend the study to the data aggregation problem, where data can not only be moved but also aggregated. We present both non-coding and coding-based solutions, and rigorously prove the performance gain by using coding.<\/p>\n","protected":false},"excerpt":{"rendered":"
NAND \ufb02ash memories have become the most widely used type of non-volatile memories. In a NAND \ufb02ash memory, every block of memory cells consists of numerous pages, and rewriting a single page requires the whole block to be erased. 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