1. A nonvolatile memory system comprising: a memory array including a plurality of cells for storing a modulated plurality of data bits and a plurality of parity bits that are calculated from the plurality of data bits according to an encoding scheme; a demodulator for reading the plurality of cells and deriving raw likelihood values corresponding to the plurality of data bits and the plurality of parity bits, wherein the demodulator is further operable to read each memory cell using a predetermined pattern of read operations, the pattern having at least one area of higher density and one area of lower density; and a decoder for receiving the raw likelihood values and calculating output likelihood values therefrom using a decoding scheme that corresponds to the encoding scheme.