Data movement in flash memories

NAND flash memories are the most widely used non-volatile memories, and data movement is common in flash storage systems. We study data movement solutions that minimize the number of block erasures, which are very important for the efficiency and longevity of flash memories. To move data among n blocks with the help of ?? auxiliary blocks, where every block contains m pages, we present algorithms that use ??(n ?? min{m, log_?? n}) erasures without the tool of coding. We prove this is almost the best possible for non-coding solutions by presenting a nearly matching lower bound. Optimal data movement can be achieved using coding, where only ??(n) erasures are needed. We present a coding-based algorithm, which has very low coding complexity, for optimal data movement. We further show the NP hardness of both coding-based and non-coding schemes when the objective is to optimize data movement on a per instance basis.