An example method is provided that includes receiving a representation of a codeword that includes a plurality of bits, and associating the bits with a respective plurality of one-bit hard-bit values representing the bits and multiple-bit soft-bit values representing measures of reliability of respective hard-bit values. The method may include determining whether participating bits for a particular parity-check equation from the plurality of parity check equations satisfy the particular parity-check equation. The method may further include determining, based on whether the particular parity-check equation is satisfied, a magnitude of a reliability modification to one or more reliability values associated with at least one of the participating bits. The method may also include modifying the one or more reliability values by the magnitude of the reliability modification.