Methods and apparatus are provided for detection and decoding in flash memories with error correlations for a plurality of bits within a sliding window. Data from a flash memory device is processed by obtaining one or more read values for a plurality of bits from one or more pages of the flash memory device; converting the one or more read values for the plurality of bits to a non-binary log likelihood ratio based on a probability that a given data pattern was written to the plurality of bits when a particular pattern was read from the plurality of bits; and decoding the plurality of bits using a binary decoder. The non-binary log likelihood ratio captures one or more of intra-page correlations and/or intra-cell correlations. A least significant bit and a most significant bit of a given cell can be independently converted and/or jointly converted to the non-binary log likelihood ratio.