1. A nonvolatile memory system comprising: a memory array including a plurality of cells that store a 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 that reads the plurality of cells and derives raw likelihood values corresponding to the plurality of data bits and the plurality of parity bits; and a decoder that receives the raw likelihood values and calculates output likelihood values therefrom using the encoding scheme.