Rewriting codes for flash memories based upon lattices, and an example using the E8 lattice

A rewriting code construction for flash memories based upon lattices is described, where the values stored in flash cells correspond to lattice points. This construction encodes information to lattice points in such a way that data can be written to the memory multiple times without decreasing the cell values. The construction partitions the flash memory's cubic signal space into blocks, which aids with encoding. The minimum number of writes is approximately linear in one of the code parameters. Using the E8 lattice as an example, the average number of writes can be increased by introducing randomization in the encoding.