Multidimensional flash codes

Flash memory is a non-volatile computer memory comprised of blocks of cells, wherein each cell can take on q different levels corresponding to the number of electrons it contains. Increasing the cell level is easy; however, reducing a cell level forces all the other cells in the same block to be erased. This erasing operation is undesirable and therefore has to be used as infrequently as possible. We consider the problem of designing codes for this purpose, where k bits are stored using a block of n cells with q levels each. The goal is to maximize the number of bit writes before an erase operation is required. We present an efficient construction of codes that can store an arbitrary number of bits. Our construction can be viewed as an extension to multiple dimensions of the earlier work of Jiang and Bruck, where single-dimensional codes that can store only 2 bits were proposed.