1. A method for soft-in, soft-out (SISO) decoding implemented by an information processing system that comprises hardware, the method comprising: accessing, at the information processing system, initial soft information on a series of data units, the data units being processed under a coding scheme, wherein the initial soft information comprises a plurality of confidence levels for each data unit; using, at the information processing system, a cyclic graphical model to represent the coding scheme, wherein the cyclic graphical model comprises a plurality of variables, wherein conditional values for the variables in the graphical model are set over a total number of first conditions representing a total number of permutations of the plurality of variables; obtaining, at the information processing system, cycle-free graphical models for a plurality of second conditions allowable by the coding scheme, wherein the number of obtained cycle-free graphical models is less than the total number of the first conditions; and generating, at the information processing system, soft-out decision information by using information comprising the obtained cycle-free graphical models and the initial soft information, wherein the soft-out decision information comprises revised confidence levels for each data unit.