Information representation and coding for nonvolatile memories

A memory device having a plurality of cells, each of which stores a value, where the values of the cells are mapped to discrete levels and the discrete levels represent data, is programmed by determining a maximum number of cell levels in the memory device, and determining the set of values that are associated with each of the cell levels. The maximum number of cell levels for the memory device is determined by an adaptive programming system connected to the memory device, based on a plurality of cell values attained by at least one cell of the memory device, in response to voltage applied by the adaptive programming system to the cells of the memory device. The adaptive programming system associates, for each of the cell levels, a different set of cell values of the plurality of cell values attained by the cells to which voltage is applied. This technique increases the number of cell levels that can be configured in a memory device as compared with conventional techniques, and increases the number of data values that can be programmed into the cells of a memory device.U