2-Cell t-Write Codes for Multilevel Flash Memories
A. K. Bhatia, Aravind R. Iyengar, Paul H. Siegel · 2011
cells. We extend the work in [1] and invoke the continuous approximation to obtain worst-case sum-rate and symmetric-write optimal t-write regions for two cells supporting continuous levels. We show that the optimal write regions for t writes on n cells is given by a n-dimensional hyperbola. Based on these results, we derive code constructions for two cells that support q discrete levels to achieve good sum rates over multiple writes per erase. We show that rates achieved by the proposed codes for cells with a large number of discrete levels are well approximated by the rates estimated through the continuous approximation. We also provide a general encoding scheme for a 2-cell t-write code.